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Full-Text Articles in Computer Sciences
On Semigroups With Lower Semimodular Lattice Of Subsemigroups, Peter R. Jones
On Semigroups With Lower Semimodular Lattice Of Subsemigroups, Peter R. Jones
Mathematics, Statistics and Computer Science Faculty Research and Publications
The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green's relation J is trivial have this property, a description in such terms is natural. In the case of periodic semigroups—a case that turns out to include all eventually regular semigroups—the characterization becomes quite explicit and yields interesting consequences. In the general case, …
Lower Semimodular Inverse Semigroups, Ii, Peter R. Jones, Kyeong Hee Cheong
Lower Semimodular Inverse Semigroups, Ii, Peter R. Jones, Kyeong Hee Cheong
Mathematics, Statistics and Computer Science Faculty Research and Publications
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 …