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He, Yong; Shao, Fang; Li, Shiqun; Gao, Wei

On left \(C\)-\(\mathcal U\)-liberal semigroups. (English) Zbl 1157.20334

Czech. Math. J. 56, No. 4, 1085-1108 (2006).
Summary: The equivalence \(\widetilde{\mathcal Q}^U\) on a semigroup \(S\) in terms of a set \(U\) of idempotents in \(S\) is defined. A semigroup \(S\) is called a \(\mathcal U\)-liberal semigroup with \(U\) as the set of projections and denoted by \(S(U)\) if every \(\widetilde{\mathcal Q}^U\)-class in it contains an element in \(U\). A class of \(\mathcal U\)-liberal semigroups is characterized and some special cases are considered.

Cited in 2 Documents

MSC:

20M10 General structure theory for semigroups

Keywords:

equivalences; left liberal semigroups; left semi-spined products; idempotents
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\textit{Y. He} et al., Czech. Math. J. 56, No. 4, 1085--1108 (2006; Zbl 1157.20334)
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