Abstract: All rings considered below are commutative with unit, and all modules are unital. For any positive integer n, we say that an R-module M is n-presented whenever there is an exact sequence: of R-modu...

Abstract: We establish that the derived Witt group is isomorphic to the usual Witt group when 2 is invertible. This key result opens the Ali Baba's cave of triangular Witt groups, linking the abstract results of Part I to classical questions for the usual Witt group. For commercial purposes, we survey the future applications of triangular Witt groups in the introduction. We also establish a connection between odd-indexed Witt groups and formations. Finally, we prove that over a commutative local ring in which 2 is a unit, the shifted derived Witt groups are all zero but the usual one.

Abstract: SUMMARY Quadrilateral 7nite elements are generally constructed by starting from a given 7nite dimensional space of polynomials ˆ V on the unit reference square ˆ K. The elements of ˆ V are then transformed by using the bilinear isomorphisms FK which map ˆ K to each convex quadrilateral element K. It has been recently proven that a necessary and su2cient condition for approximation of order r +1 inL 2 and r in H 1 is that ˆ V contains the space Qr of all polynomial functions of degree r separately in each variable. In this paper several numerical experiments are presented which con7rm the theory. The tests are taken from various examples of applications: the Laplace operator, the Stokes problem and an eigenvalue problem arising in ?uid-structure interaction modelling. Copyright ? 2001 John Wiley & Sons, Ltd.

Abstract: A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. We show that if R is (left principally) quasi-Baer and G is an ordered monoid, then the monoid ring RG is again (left principally) quasi-Baer. When R is (left principally) quasi-Baer and G is an ordered group acting on R, we give a necessary and sufficient condition for the skew group ring R♯G to be (left principally) quasi-Baer.

Abstract: We extend the Larson-Sweedler theorem to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf algebra is autonomous monoidal with semisimple unit and invertible modules. We also reveal the connection of invertible modules to left and right grouplike elements in the dual weak Hopf algebra. Defining distinguished left and right grouplike elements we derive the Radford formula for the fourth power of the antipode in a weak Hopf algebra and prove that the order of the antipode is finite up to an inner automorphism by a grouplike element in the trivial subalgebra A^T of the underlying weak Hopf algebra A.

Abstract: In this paper, we show that if R satisfies unit 1-stable range, then so does M n (R) for any n ≥ 1. Also we prove that if R has many unit-regular elements, then so does M n (R) for any n ≥ 1. Finally, we show that if for any x, y ∈ R there exists a u ∈ U (R) such that x−u, y−u −1 ∈ U (R), then for any X, Y ∈ M n (R), there exists a U ∈ GL n (R) such that X–U, Y−U −1 ∈ GL n (R).

Abstract: This papor concludes the work begun in (1J. It considers unit forms, i.e. positiva definite integral quadratic froms with unitary coefficients in the quadratic terms. The equivalence classes of connected unit forms are given by Dynkin diagrams. The paper presents a characterization of positive unit forms which are equivalent to B n for some integer n in terms of the associated bigraphs and gives a list for the case EG-

Abstract: AllergyVolume 56, Issue 1 p. 84-85 Selective immediate hypersensitivity to ceftazidime† A. Romano, A. Romano Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. Di Fonso, M. Di Fonso Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. C. Artesani, M. C. Artesani Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. Viola, M. Viola Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorF. B. Adesi, F. B. Adesi Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorA. Venuti, A. Venuti Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this author A. Romano, A. Romano Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. Di Fonso, M. Di Fonso Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. C. Artesani, M. C. Artesani Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorM. Viola, M. Viola Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorF. B. Adesi, F. B. Adesi Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this authorA. Venuti, A. Venuti Unità di AllergologiaComplesso Integrato ColumbusVia G. Moscati, 3100168 Rome, ItalyTel. 00 39 06 3503782Fax: 00 39 06 3503653E-mail: [email protected]Search for more papers by this author First published: 23 September 2008 https://doi.org/10.1034/j.1398-9995.2001.00921.xCitations: 14 † Anaphylaxis with positive intradermal skin test. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article.Citing Literature Volume56, Issue1January 2001Pages 84-85 RelatedInformation

Abstract: Underp2 (0;1 )a nd Mmapw(z )=( w z)=(1 wz), a holomorphic function on the unit disk4 is said to be ofQp;0 class if limjwj!1Ep(f;w )=0 , where

Abstract: Recently, a proof of the existence of a flat cover of any module over an arbitrary associative ring with unit has been finally given (see 4-5) In this paper we prove the existence of flat covers in the category of graded modules over a graded ring Some graded theoretical machinery is introduced to make the proof possible and new graded homological tools are developed

Abstract: Abstract The Medicines Monitoring Unit (MEMO) is a University‐based organization that uses record‐linkage techniques to construct an observational database for the population of Tayside, Scotland (approximately 400 000 people). This contains healthcare data indexed by a unique identifier, including data on all prescriptions dispensed, which facilitates pharmacoepidemiological (and other) research. It has hitherto been possible to carry out drug safety studies in the entire population, with access to original medical records of patients where necessary, that have satisfied ethical concerns and confidentiality legislation. However, the recent UK Data Protection Act 1998 (which enforces the 1995 European Directive on Data Protection) has important implications for MEMO's research. The Act has necessitated changes to the way in which research studies are carried out, with MEMO's objective being to ensure that research can continue while protecting the rights and privacy of individual patients. This involves anonymization of data, seeking specific ethical approval for research studies and obtaining relevant permissions from ‘Caldicott Guardians’, as described in this article. Copyright © 2001 John Wiley & Sons, Ltd.

Abstract: We extend the Larson-Sweedler theorem for weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We establish the autonomous monoidal category of the modules of a weak Hopf algebra A and show the semisimplicity of the unit and the invertible modules of A. We also reveal the connection of these modules to left/right grouplike elements in the dual weak Hopf algebra A^.

Abstract: A ring network element and the ring network architectures it enables. According to one embodiment of the invention, a single network element includes a full TDM cross-connect and a multiple ring unit. The full TDM cross-connect is coupled to every line card slot in the single network element with the same amount of bandwidth connection. In addition, the full TDM cross-connect is programmable on an STS-1 basis. The multiple ring unit allows for the simultaneous support of multiple TDM rings.

Abstract: We consider units of orders in a simple algebra A of finite dimension over the rational field. Such A can be written as A = Mn(D) where D is a skewfield (say of index d). Let K denote the centre of A (and D), R the integral closure of K, Λ an R-order in A, Γ = Λ× the group of units of Λ and SΓ the kernel of the reduced norm map nr : A → K on Γ. Two groups G and H are said to be commensurable (denoted G ∼ H) if they have a common subgroup of finite index. Since Γ ∼ R× × SΓ, the difficulty of Γ is concentrated in SΓ. It is well known that SΓ ∼ 1 if and only if A = K or A = D is a totally definite quaternion algebra. In the search for a structure theorem it is natural to envisage group theoretical constructions which produce “large” groups out of “small” ones. The most common examples are direct products, semidirect products, free products, amalgams and HNN extensions. We show that these constructions apply to unit groups only in very few cases of small dimension, the majority of which are well-known already. This demonstrates how far away we still are from an understanding of general unit groups.

Abstract: The purpose of this paper is to provide a proper identification of normal, irreducible, regular algebraic monoids (regular is defined in §2). The results of [3,4] suggest that we should be able to find a classification of these monoids in terms of their unit groups, and related toroidal data. And that is what we accomplish here. Assume that M is a normal, regular, algebraic monoid with unit group G . All our algebraic monoids are defined over an algebraically closed field of arbitrary characteristic. Let e ∈M be a minimal idempotent, and define

Abstract: PROBLEM TO BE SOLVED: To cope flexibly with specification changes by a customer for such attachment units mounted on the side face of the circuit breaker, such as an auxiliary switch, alarm switch or the like SOLUTION: In a common insulated container, consisting of a unit case 31 and a unit cover 32, the auxiliary switch 33 and the alarm switch 34 are built in together, an auxiliary contact support 37 and an alarm contact support 43 that are made to retain respective moving contacts 36 and 42 are guided by a ridge 31b of the unit case 31, so as to make a linear motion on the same line An auxiliary unit, enclosing the both auxiliary switch 33 and alarm switch 34, is easier for changing specifications in comparison to that, in which they are mounted on the circuit breaker as separate units, the and manufacturing cost can be suppressed because the most components are used commonly

Abstract: Let AMB be a QF-bimodule, A a left Artinian ring, B a right Artinian ring, G a semigroup with a unit element (a monoid). Let MG be the set of all functions on G with values in M. Consider MG as an (AG, BG)-bimodule over the semigroup rings AG and BG. It is proved that the annihilator maps I → rMG (I) and R → lAG (R) are mutually inverse bijective Galois correspondences between the set of finitely cogenerated left ideals I ⊆ AG and the set of right BG-submodules R ⊆ MG finitely generated over B. The maps J → lMG (J) and L → rAG (L) are mutually inverse bijective Galois correspondences between the set of finitely cogenerated right ideals J ⊆ AG and the set of left AG-submodules L ⊆ MG finitely generated over A. This result also makes it possible, starting from a given QF-bimodule A MB , to construct new QF-bimodules AG/ISBG/J as bimodules of functions on a semigroup with values in M.

Abstract: We show the di erence between the set of Bre sar generalized derivations and the set of generalized derivations as K-modules over a commutative ring K. We also refer to the extendability of Bre sar generalized derivations. Moreover, we apply the results to generalized Jordan derivations.

Abstract: In this note it is shown that the dual algebra generated by a completely non-unitary subnormal tuple S with an isometric w*-continuous H∞-functional calculus over the unit polydisc satisfies the factorization property ( A 1 , ℵ 0 ). This observation is used to deduce that S is reflexive and possesses a dense set of vectors generating an analytic invariant subspace.

Abstract: Let G be an arbitrary group. For any nontrivial bicyclic unit u ∈ G, a necessary and sufficient condition for which the pair {u, uf } generates a nonabelian free group is given. Moreover, it is proved that the above pair always generates a torsionfree subgroup of the unit group U( G) and the structure of this subgroup ⟨u, uf ⟩ is characterized.

Abstract: We show that an loop has a torsion-free normal complement in the loop of normalized units of its integral loop ring. We also investigate whether an loop can be normal in its unit loop. Over fields, this can never happen.

Abstract: Department of Mathematics, Hunan Normal University, Changsha 410006, P.R. ChinaE-mail: chyzxl@sparc2.hunnu.edu.cn2000 Mathematics Subject Classification: 16U99, 16E50Abstract. In this paper, we show that if rings A and B are –s;2ƒ-rings, then so is the ring of aMorita context –A;B;M;N;c;fƒ. Also we get analogous results for unit 1-stable rangesand GM-rings. These give new classes of rings satisfying such stable range conditions.Keywords: Morita context, unit 1-stable range, GM-ring

Abstract: The purpose of this paper is to exhibit a new family of real bicyclic biquadratic fields K for which we can write the Hasse unit index of the group generated by the units of the three quadratic subfields in the unit group EK of K. As a byproduct, one can explicitly relate the class number of K with the product of the class numbers of the three quadratic subfields.

Abstract: Abstract In a social order that is deeply racialized, any policy that invokes race as a sign, a mark of, rather than as grounds for preferential treatment, even where justified, is likely to be used to exacerbate racial tensions and divides, to magnify whatever racially characterized tensions and ambivalences there are.

Abstract: The bearing has a fixed outer ring (2) and rotating inner ring (3). A magnetic coder (5) is attached to the inner ring by a support (6) and is in close proximity to a receiving and measuring element (7) fixed to the outer ring. A radio transmitter (14) is included with the measuring element and uses an antenna (20) to communicate with a radio receiver and calculator which may be located anywhere in the vehicle