Journal Article10.1142/S0218196701000541
Orthodox transversals of regular semigroups
J. F. Chen,Y. Q. Cuo +1 more
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TL;DR: The general case of orthodox transversals is considered, it is proved that the semibands Ī and generated by I and Λ respectively are bands, and somewhat interesting generalizations of properties on orthodox semigroups are given.
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Abstract: Orthodox transversals were introduced by the first author as a generalization of inverse transversals [Comm. Algebra 27(9) (1999), pp. 4275–4288]. One of our aims in this note is to consider the general case of orthodox transversals. The main results are on the sets I and Λ, two components of regular semigroups with orthodox transversals. We prove that the semibands Ī and generated by I and Λ respectively are bands. Also somewhat interesting generalizations of properties on orthodox semigroups are given; another aim in this note is to give some examples illustrating the situations that the class of regular semigroups with orthodox transversals properly includes the class of regular semigroups with inverse transversals as well as the class of orthodox semigroups.
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Citations
The product of quasi-ideal refined generalised quasi-adequate transversals
TL;DR: In this paper, an interesting characterization for a generalised quasi-adequate transversal to be refined is acquired, and it is shown that the product of every two quasi-ideal RGQA transversals of the abundant semigroup S satisfying the regularity condition is a quasi-ideal RGQAs of S, and that all quasiideal RFQAs compose a rectangular band.
Semi-abundant Semigroups with Quasi-Ehresmann Transversals
TL;DR: In this article, a structure theorem of semi-abundant semigroups with quasi-ideal strong quasi-Ehresmann transversals is obtained. But it is not a generalization of Chen's results.
On refined generalised quasi-adequate transversals
Xiangjun Kong,Pei Wang +1 more
TL;DR: In this article, the concept of refined generalised quasi-adequate transversals, for short, RGQA transversal, was introduced and characterized for abundant semigroups.
Abundant semigroups with weakly simplistic RGQA transversals
Pei Wang,Xiangjun Kong +1 more
TL;DR: In this paper , the necessary and sufficient condition for the RGQA transversal to be bands is investigated, and the structure theorem for an abundant quasi-adequate semigroup with a weakly simplistic RGQAs is established.
Regular semigroups with multiplicative orthodox transversals
Pei Wang,Xiangjun Kong +1 more
- 01 Jan 2010
TL;DR: In this paper, the concept of multiplicative orthodox transversals is introduced and some properties on multiplicative orthogonality are investigated, and two examples are given to show a regular non-orthodox and an orthodox semigroup with a multiplicative transversal, respectively.
References
Regular semigroups with a multiplicative inverse transversal
T. S. Blyth,R. McFadden +1 more
TL;DR: In this paper, an inverse transversal of a regular semigroup S is defined as an inverse subsemigroup that contains a single inverse of every element of S. A certain multiplicative property (which in the case of a band is equivalent to normality) is imposed on an inverse Transversal and a complete description of the structure of S is obtained.
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On the construction of a class of regular semigroups
T.S Blyth,R. McFadden +1 more
TL;DR: In this paper, the internal structure of regular semigroups that have a greatest idempotent, and on which Green's relations R and L are regular, is described.
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