A nilpotent-generated semigroup associated with a semigroup of full transformations-Reference-Cited by-同舟云学术

A nilpotent-generated semigroup associated with a semigroup of full transformations

Published:1988 Issue:1-2 Volume:108 Page:181-187
ISSN:0308-2105
Container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
language:en
Short-container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Author:

Howie John M.,Marques-Smith M. Paula O.

Abstract

SynopsisLet X be a set with infinite regular cardinality m and let ℱ(X) be the semigroup of all self-maps of X. The semigroup Qm of ‘balanced’ elements of ℱ(X) plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of ℱ(X), as does the subset Sm of ‘stable’ elements, which is a subsemigroup of Qm if and only if m is a regular cardinal. The principal factor Pm of Qm, corresponding to the maximum ℱ-class Jm, contains Sm and has been shown in [7] to have a number of interesting properties.Let N2 be the set of all nilpotent elements of index 2 in Pm. Then the subsemigroup (N2) of Pm generated by N2 consists exactly of the elements in Pm/Sm. Moreover Pm/Sm has 2-nilpotent-depth 3, in the sense that

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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