A Munn type representation of abundant semigroups with a multiplicative ample transversal

作者：Wang, Shoufeng^*

来源：Periodica Mathematica Hungarica, 2016, 73(1): 43-61.

DOI：10.1007/s10998-016-0124-5

• The Munn semigroup of an admissible quadruple
• Multiplicative ample transversal
• Fundamental abundant semigroup

The celebrated construction by Munn of a fundamental inverse semigroup from a semilattice E provides an important tool in the study of inverse semigroups and ample semigroups. Munn's semigroup has the property that a semigroup is a fundamental inverse semigroup (resp. a fundamental ample semigroup) with a semilattice of idempotents isomorphic to E if and only if it is embeddable as a full inverse subsemigroup (resp. a full subsemigroup) into . The aim of this paper is to extend Munn's approach to a class of abundant semigroups, namely abundant semigroups with a multiplicative ample transversal. We present here a semigroup from a so-called admissible quadruple that plays for abundant semigroups with a multiplicative ample transversal the role that plays for inverse semigroups and ample semigroups. More precisely, we show that a semigroup is a fundamental abundant semigroup (resp. fundamental regular semigroup) having a multiplicative ample transversal (resp. multiplicative inverse transversal) whose admissible quadruple is isomorphic to if and only if it is embeddable as a full subsemigroup (resp. full regular subsemigroup) into . Our results generalize and enrich some classical results of Munn on inverse semigroups and of Fountain on ample semigroups.

• 出版日期2016-9
• 单位云南师范大学