TL;DR: In this paper, a c -normal condition on minimal subgroups is used to characterize the structure of a finite group through the theory of formations, and the results show that the properties of the subgroups of a group can influence its structure.

TL;DR: In this article, it was shown that many of the concepts of weak ω-category theory arise in the natural development of category theory internal to the petit 1 topos Glob of globular sets.

TL;DR: In this paper, a modified notion called multitopic set is introduced, which is a mild generalization of the same-named notion introduced by Joachim Lambek in 1969, inspired by the concept of opetopic set introduced by John C. Baez and James Dolan.

TL;DR: The rigid dualizing complex of A was introduced by Van den Bergh as discussed by the authors, who proved that it is (U ( g )⊗⋀ n g )[n], where n = dim g.

TL;DR: In this paper, the authors apply the characterisation of the case of the category of ontological spaces and apply it to the categories of Cartesian closed and non-cartesian closed.

TL;DR: In this article, the authors deal with representations of Lie algebras of reductive groups in prime charateristic settings, and obtain results previously known only for restricted representations (on graded structures, filtrations, translation functors) are extended to representations with a non-zero p -character.

TL;DR: The notion of weak subobject was introduced by Grandis (Cahiers Topologie Geom. Differentielle Categoriques 38 (1997) 301-326) as an extension of the notion of subobject, adapted to homotopy categories or triangulated categories, and well linked with their weak limits as mentioned in this paper.

TL;DR: An algorithmic procedure computing the polynomials and constants occurring in a Bezout identity, whose complexity is polynomial in the geometric degree and linear in the height of the system, is shown.

TL;DR: In this article, the representation theory of self-injective algebras which admit Galois coverings by the repetitive algesbras of tilted algebases of wild type was developed.

TL;DR: In this paper, it was shown that R / P h has a linear resolution for all h and hence the Hilbert function of R/P h is also a linear Hilbert function.

TL;DR: In this article, the authors characterize α-soluble locales, i.e. locales whose αth dissolution is Boolean, for α≤4, and give a sufficient condition for insolubility which implies that the only metrizable spaces with a Boolean coreflection are the scattered ones.

TL;DR: A characterization of quasi-Baer rings with a sheaf representation is given in this article, where it is shown that a ring R with a complete set of triangulating idempotents has such a representation if and only if R is a finite direct sum of prime rings.

TL;DR: In this article, it was shown that a good determinantal scheme of codimension r+1 is equivalent to being the zero-locus of a regular section of the dual of a first Buchsbaum-Rim sheaf of rank r + 1.

TL;DR: In this article, the local cohomology modules supported on a monomial ideal I of the local regular ring R =k[[x 1,…,x n ]], where k is a field of characteristic zero, were studied.

TL;DR: In this paper, the authors studied tilting modules for reductive algebraic groups in prime characteristics, characterized by having filtrations both by Weyl modules and by dual Weylmodules.

TL;DR: Castro-Jimenez and Narvaez-Macarro as discussed by the authors generalize these results by adapting the theory of Grobner bases of Mora-Robbiano to the D -module case.

TL;DR: Theorem 2.2 as mentioned in this paper shows that G is not Cohen-Macaulay unless the ideals we are considering are of maximal Cohen-Mcaulay type, which is a conjecture that has been proved in Comm. Algebra 24(13) (1996) 4249-4261; Pure Appl. J.

TL;DR: In this article, the authors studied additive submonoids M of N n consisting of the solutions of a homogeneous linear diophantine equation with integer coefficients, and developed sufficient and/or necessary conditions for the half-factoriality of M.

TL;DR: In this article, it was shown that the injective dimension of a local cohomology module is bounded by the dimension of the support of the module, and that the same inequality holds also for local cohomorphology modules HiI(R).

TL;DR: In this paper, the notion of trace operators on a linearly distributive category has been introduced, which allows an object to have at most one trace structure (for a given tensor structure).

TL;DR: In this paper, a Goresky-MacPherson formula for subspace arrangements in characteristic p is established and a special form of the formula is applied to provide a lower bound on the arithmetical rank of monomial ideals.

TL;DR: In this paper, the problem of determining up to graded isomorphism of the modules in a minimal free resolution of a fat point subscheme Z =m 1 p 1 +⋯+m r p r ⊂ P 2 for general points p 1,…,p r.

TL;DR: In this paper, it was shown that for a factorization linearly ordered small category B, the category of discrete Giraud-Conduche fibrations over B is a (model generated) topos.

TL;DR: In this paper, the authors studied various algebraic and topological conditions on a group G which imply the existence of a suitable set for G as well as the restraints imposed by such a set.

TL;DR: In this paper, a sharp bound for the regularity index of arbitrary fat points in P 3 was given, which generalizes the Segre bound for regularity of points in general position.

TL;DR: In this article, the authors find some simple combinatorial criteria for a string algebra to be tilted or quasi-tilt, which will enable one to construct a lot of new examples of tilted algebras.

TL;DR: In this paper, it was shown that the variety of all the pairs (A,B) of n×n matrices over an algebraically closed field K such that A,B]=0, rank B≤h is irreducible for all n and h = 0, 0, n.

TL;DR: In this article, the outer automorphism group of a group G, denoted Out G, is defined as the quotient group Aut G/ Inn G. If M is any group, then there exists a torsion-free, metabelian group G with trivial center such that Out G≅M.

TL;DR: In this paper, the authors investigated the connections between the weak π-regularity and the maximality of prime ideals in 2-primal rings, right quasi-duo rings and PI-rings, respectively.