LOWER SEMIMODULAR INVERSE SEMIGROUPS, II

作者：Cheong Kyeong Hee; Jones Peter R^*

来源：Communications in Algebra, 2011, 39(3): 955-971.

DOI：10.1080/00927871003614439

• Inverse semigroup
• Semimodular
• Subsemigroup lattice

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 (sic)(o)(E(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 (sic)(o)(E(S)), respectively, where ES 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 (sic)(o)(E(S)) 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 (sic)(o)(E(S)), with the latter being substantially richer.

• 出版日期2011