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Howson's Property for Semidirect Products of Semilattices by Groups

Soares, Filipa; Silva, Pedro V.

Communications in Algebra, 44 (2016), 2482-2494

An inverse semigroup S is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of S is finitely generated. Given a locally finite action ? of a group G on a semilattice E, it is proved that E*?G is a Howson inverse semigroup if and only if G is a Howson group. It is also shown that this equivalence fails for arbitrary actions.