Varieties of Boolean inverse semigroups

JOURNAL OF ALGEBRA

卷:511

Article

Wehrung, Friedrich¹ 

[1] Univ Caen Normandie, Dept Math, CNRS UMR 6139, LMNO, F-14032 Caen, France

关键词: Semigroup;    Monoid;    Inverse;    Boolean;    Bias;    Variety;    Group;    Wreath product;    Additive homomorphism;    Conical;    Refinement monoid;    Index;    Type monoid;    Generalized rook matrix;    Fully group-matricial;    Radical;    Congruence;    Residually finite;   

DOI  :  10.1016/j.jalgebra.2018.06.018

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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