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- W3022020370 abstract "The authorsβ description of the inverse semigroups S for which the lattice ββ±(S) of full inverse subsemigroups is lower semimodular is used to describe those for which (a) the lattice β(S) of all inverse subsemigroups or (b) the lattice πo(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 ββ±(S) with β(E S ), or πo(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, β(E) is in fact always lower semimodular, and πo(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, β(S) and πo(S), with the latter being substantially richer." @default.
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- W3022020370 date "2011-03-16" @default.
- W3022020370 modified "2023-09-24" @default.
- W3022020370 title "Lower Semimodular Inverse Semigroups, II" @default.
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- W3022020370 doi "https://doi.org/10.1080/00927871003614439" @default.
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