Locally finite monoids in finitely based varieties. (English) Zbl 1494.20083
Summary: It is shown that given any finite system of monoid identities, it is decidable if the class of locally finite monoids that satisfy the system is a variety. This answers an open problem of M. V. Sapir [Combinatorial algebra: syntax and semantics. With contributions by Victor S. Guba and Mikhail V. Volkov. Cham: Springer (2014; Zbl 1319.05001)].
MSC:
20M07 | Varieties and pseudovarieties of semigroups |
20M05 | Free semigroups, generators and relations, word problems |