Results 21 to 30 of about 54 (36)
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A Biordered Set Representation of Regular Semigroups
Acta Mathematica Sinica, English Series, 2005Following the milestone works by \textit{W. D. Munn} [Q. J. Math., Oxf. II. Ser. 21, 157-170 (1970; Zbl 0219.20047)] and \textit{T. E. Hall} [Pac. J. Math. 39, 677-686 (1971; Zbl 0232.20124)] for any regular biordered set \(E\), by using biorder isomorphisms between the \(\omega\)-ideals on \(E\), the authors construct a fundamental regular semigroup \(
Yu, Bingjun, Xu, Mang
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Biordered Sets and Regular Rings
Springer Proceedings in Mathematics and Statistics, 2015Biordered sets were introduced in [3] to describe the structure of regular semigroups. In [1] it is shown that the ideals of a regular ring forms a complemented modular lattices. Here we describe the biordered set of such a regular ring.
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Biordered Sets of Regular Semigroups with Inverse Transversals1
Southeast Asian Bulletin of Mathematics, 2001In a regular semigroup S, an inverse subsemigroup S° of S is called an inverse transversal of S if S° contains a unique inverse x° of each element x of S. An inverse transversal S° of S is called a Q-inverse transversal of S if S° is a quasi-ideal of S.
Xilin Tang
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Locally Ordered Biordered Sets
Communications in Algebra, 2010It is shown that a representation φ introduced by Easdown and Hall [10] affords a natural construction of biordered sets that are locally like semilattices from those that are locally like ordered sets. If E is a biordered set which is locally like an ordered set, then the biordered set E(⟨Eφ⟩) is locally like a semilattice. In particular, the property
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Biordered Sets of Eventually Regular Semigroups
Proceedings of the London Mathematical Society, 1984\textit{K. S. S. Nambooripad} [Mem. Am. Math. Soc. 224 (1979; Zbl 0457.20051)] introduced the concept of a biordered set as a partial algebra satisfying several axioms, and proved that the set of idempotents of any semigroup forms a biordered set in a natural way.
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SUBGROUPS OF THE FREE SEMIGROUP ON A BIORDERED SET IN WHICH PRINCIPAL IDEALS ARE SINGLETONS
Communications in Algebra, 2002ABSTRACT Easdown has conjectured that the subgroups of the free semigroup on an arbitrary biordered set are free. In this note a weaker conjecture is verified. It is shown that the subgroups of the free semigroup on a biordered set in which principal ideals are singletons are free.
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2021
This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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This thesis was scanned from the print manuscript for digital preservation and is copyright the author. Researchers can access this thesis by asking their local university, institution or public library to make a request on their behalf. Monash staff and postgraduate students can use the link in the References field.
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Biordered Sets of Regular Semigroups with Inverse Transversals
Southeast Asian Bulletin of Mathematics, 2001In a regular semigroup \(S\), an inverse subsemigroup \(S^\circ\) of \(S\) is called an inverse transversal of \(S\) if \(S^\circ\) contains a unique inverse \(x^\circ\) of each element \(x\) of \(S\). The subject of this paper is the class of biordered sets of regular semigroups with inverse transversals, known throughout as IT-biordered sets.
Tang, Xilin, Wang, Limin
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