On + - Abundant Semigroups

By Minhui Luo. 2002

221 citations recorded by the source corpus.

How researchers see this paper

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On equivalence of matrices (2016, unknown): “We refer readers to [27], [24], [18] for concepts and properties.”
Beyond regular semigroups (2016, methodology): “The purpose of this chapter is to show that the trace of a weakly B-orthodox semigroup is a primitive weakly B-orthodox semigroup and investigate primitive weakly B-orthodox semigroups via blocked Rees matrix semigroups, which are introduced in [10].”
RESTRICTION AND EHRESMANN SEMIGROUPS (2011, unknown): “We recall that a semigroup S is abundant [12] if every R * -class and L * -class contains an idempotent, where R * is defined by the rule that a R * b if and only if for all x, y ∈ S 1 , xa = ya ⇔ xb = yb and L * is the dual.”
On generalized inverses and Green's relations (2009, unknown): “1 in [3], this is equivalent to (xa = ya ⇐⇒ xb = yb ∀x, y ∈ S(1)).”
Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section (2004, background): “As stated in [3], where the concept was introduced, the word “abundant” comes from the fact that such semigroups have a plentiful supply of idempotents.”
An Invitation to C-semigroups (2001, background): “This also follows by noting that on a regular semigroup L̃ = L (see [8] for example).”