Results 61 to 70 of about 4,910,326 (80)

Biordered sets and fundamental semigroups

Semigroup Forum, 2010
For any abstract biordered set (boset) \(E\) is constructed a semigroup \(T_E\) such that \(T_E\) and its symmetric subsemigroups are fundamental and generated by regular elements; any full subsemigroup of \(T_E\) for any boset \(E\) generated by regular elements is also fundamental.
David Easdown
exaly   +3 more sources

A Biordered Set Representation of Regular Semigroups

Acta Mathematica Sinica, English Series, 2005
Following 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
exaly   +3 more sources

Biordered sets

1992
Abstract In Section 1.5 the notion of the biordered set of a semigroupS was introduced, along with the associated idea of a sandwich set of an ordered pair of idempotents,S(e,f). That an element may always be drawn fromS(e,f) in caseS is regular was used implicitly in Theorem 1.4.17, and sandwich sets were also used to describe those ...
Peter M Higgins
exaly   +2 more sources

LRT-Biordered Sets

Semigroup Forum, 2006
We give a characterization and a representation of LRT-biordered sets. IT-biordered sets form a subclass of the class of all LRT-biordered sets: they are the biordered sets of idempotents of regular semigroups with an inverse transversal.
Xilin Tang
exaly   +2 more sources

On maximal subgroups of idempotent-generated semigroups associated with biordered sets [PDF]

, 2021
Given any biordered set $E$, we may form the idempotent-generated semigroup $F_E$, which is generated by the set $E$, subject to the relations $ef=e*f$ whenever $e$ and $f$ are elements of $E$ and $e*f$ is a basic product. Easdown proved in 1985 that the biordered set of $F_E$ is biorder isomorphic to $E$, thus demonstrating that the biordered set ...
Gardiner, Sean Bruce Gilbert
openaire   +3 more sources

Biordered Sets and Regular Rings

Springer Proceedings in Mathematics and Statistics, 2015
Biordered 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.
exaly   +2 more sources

Biordered Sets of Regular Semigroups with Inverse Transversals1

Southeast Asian Bulletin of Mathematics, 2001
In 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
exaly   +2 more sources

A new proof that regular biordered sets come from regular semigroups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984
SynopsisA new proof is given that all regular biordered sets come from regular semigroups.
David Easdown
openaire   +2 more sources

Locally Ordered Biordered Sets

Communications in Algebra, 2010
It 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
exaly   +2 more sources

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.
exaly   +2 more sources