Results 11 to 20 of about 93 (82)
Unit orthodox semigroups [PDF]
Glasgow Mathematical Journal, 1983 Let S be a regular semigroup. Given x ∈ S, we shall say that a ∈ S is an associate of x if xax = x. The set of associates of x ∈ S will be denoted by A(x). Now suppose that S has an identity element 1. Let H1 denote the group of units of S. Then we say that u ∈ S is a unit associate of x whenever u ∈ A(x)∩Hl. In what follows we shall write U(x) = A(x)∩=
Blyth, T. S., McFadden, R.
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Congruences on Orthodox Semigroups [PDF]
Journal of the Australian Mathematical Society, 1971 A semigroup S is called regular if a ∈ aSa for every element a in S. The elementary properties of regular semigroups may be found in A. H. Clifford and G. B. Preston [1]. A semigroup S is called orthodox if S is regular and if the idempotents of S form a subsemigroup of S.
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Open Mathematics, 2015 In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced.
Gu Ze, Tang Xilin
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Idempotent 2x2 matrices over linearly ordered abelian groups [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper we study multiplicative semigroups of $2\times 2$ matrices over a linearly ordered abelian group with an externally added bottom element. The multiplication of such a semigroup is defined by replacing addition and multiplication by join and
Valdis Laan, Marilyn Kutti
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End-regular and End-orthodox generalized lexicographic products of bipartite graphs
Open Mathematics, 2016 A graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.
Gu Rui, Hou Hailong
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Invariant semigroups of orthodox semigroups
Semigroup Forum, 1996 The paper is a continuation of a previous one of these authors [J. Algebra 169, No. 1, 49-70 (1994; Zbl 0811.06015)]. An inverse transversal of a regular semigroup \(S\) is an inverse subsemigroup \(T\) with the property that, for every \(x\in S\), \(T\) contains one and only one inverse element \(x^0\) of \(x\) in \(S\).
Blyth, T.S., Almeida-Santos, M.H.
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Flows on Classes of Regular Semigroups and Cauchy Categories
Journal of Mathematics, Volume 2019, Issue 1, 2019., 2019 We consider the structure of the flow monoid for some classes of regular semigroups (which are special case of flows on categories) and for Cauchy categories. In detail, we characterize flows for Rees matrix semigroups, rectangular bands, and full transformation semigroups and also describe the Cauchy categories for some classes of regular semigroups ...
Suha Ahmed Wazzan, Radomír Halaš
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Certain congruences on orthodox semigroups [PDF]
Pacific Journal of Mathematics, 1976 Let \(S\) be a regular semigroup and \(E\) be the set of all its idempotents. The semigroup \(S\) is called unitary semigroup if \(e,ea\in E\) implies \(a\in E\) for all \(a,e\in S\). Regular semigroups are described which are underdirect products of unitary semigroups and semilattices of groups.
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Characterizations of N(2,2, 0) Algebras
Algebra, Volume 2016, Issue 1, 2016., 2016 The so‐called ideal and subalgebra and some additional concepts of N(2, 2, 0) algebras are discussed. A partial order and congruence relations on N(2, 2, 0) algebras are also proposed, and some properties are investigated.
Fang-an Deng +4 more
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Bisimple monogenic orthodox semigroups [PDF]
Semigroup Forum, 2008 We give a complete description of the structure of all bisimple orthodox semigroups generated by two mutually inverse elements.
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