Document Type

Article

Language

eng

Format of Original

17 p.

Publication Date

2010

Publisher

Taylor & Francis

Source Publication

Communications in Algebra

Source ISSN

0092-7872

Original Item ID

doi: 10.1080/00927871003614439

Abstract

The authors’ description of the inverse semigroups S for which the lattice ℒℱ(S) of full inverse subsemigroups is lower semimodular is used to describe those for which (a) the lattice ℒ(S) of all inverse subsemigroups or (b) the lattice �o(S) of convex inverse subsemigroups has that property. In each case, we show that this occurs if and only if the entire lattice is a subdirect product of ℒℱ(S) with ℒ(E S ), or �o(E S ), respectively, where E S is the semilattice of idempotents of S; a simple necessary and sufficient condition is found for each decomposition. For a semilattice E, ℒ(E) is in fact always lower semimodular, and �o(E) is lower semimodular if and only if E is a tree. The conjunction of these results leads to quite a divergence between the ultimate descriptions in the two cases, ℒ(S) and �o(S), with the latter being substantially richer.

Comments

Accepted version. Communications in Algebra, Vol. 39, No. 3 (2011): 955-971. DOI. © 2011 Taylor & Francis. Used with permission.

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