Varieties of Boolean inverse semigroups

Abstract : In an earlier work, the author observed that Boolean inverse semigroups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of varieties of biases in terms of varieties of groups: (1) Every free bias is residually finite. In particular, the word problem for free biases is decidable. (2) Every proper variety of biases contains a largest finite symmetric inverse semigroup, and it is generated by its members that are monoids of generalized rook matrices over groups with zero. (3) There is an order-preserving, one-to-one correspondence between proper varieties of biases and certain finite sequences of varieties of groups, descending in a strong sense defined in terms of wreath products by finite symmetric groups.
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Contributeur : Friedrich Wehrung <>
Soumis le : lundi 24 octobre 2016 - 16:40:05
Dernière modification le : jeudi 7 février 2019 - 17:32:30

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Friedrich Wehrung. Varieties of Boolean inverse semigroups. Journal of Algebra, Elsevier, 2018, 511, pp.114--147. ⟨10.1016/j.jalgebra.2018.06.018⟩. ⟨hal-01386827⟩

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