Decidability of Equational Theories of Coverings of Semigroup Varieties |
| |
Authors: | V Yu Popov |
| |
Institution: | (1) The Institute of Mathematics and Mechanics of the Ural Division of the Russian Academy of Sciences, Ekaterinburg |
| |
Abstract: | For every proper semigroup variety X, there exists a semigroup variety Y satisfying the following three conditions: (1) Y covers X, (2) if X is finitely based then so is Y, and (3) the equational theory of X is decidable if and only if so is the equational theory of Y. If X is an arbitrary semigroup variety defined by identities depending on finitely many variables and such that all periodic groups of X are locally finite, then one of the following two conditions holds: (1) all nilsemigroups of X are locally finite and (2) X includes a subvariety Y whose equational theory is undecidable and which has infinitely many covering varieties with undecidable equational theories. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|