Quasi-identities of finite semigroups and symbolic dynamics
An algebra is called inherently non-finitely \((Q-)\) based if it is not contained in any locally finite and finitely based (quasi-)variety. \textit{M. V. Sapir} first proved that there exist finite inherently non-finitely based semigroups [Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 2, 319-340 (1987; Zbl 0646.20047)]\ and then effectively described them all [Mat. Sb., Nov. Ser. 133, 154-166 (1987; Zbl 0634.20027)]. In the paper under review the authors show that, in strong contrast with the variety case, no finite semigroup is inherently non-finitely \(Q\)-based. The proof makes essential use of the connection between Burnside type problems for semigroups and symbolic dynamics established in the first of the cited papers by M. V. Sapir.
finite inherently non-finitely based semigroups
scientific article; zbMATH DE number 836171
scientific article