Equational Theories for Classes of Finite Semigroups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Equational Theories for Classes of Finite Semigroups

Authors:	V Yu Popov

Institution:	(1) Marshala Zhukova 11-6, Ekaterinburg, 620077

Abstract:	It is proved that there exists an infinite sequence of finitely based semigroup varieties $\mathfrak{A}_{\text{1}} \subset \mathfrak{B}_{\text{1}} \subset \mathfrak{A}_{\text{2}} \subset \mathfrak{B}_{\text{2}} \subset ...$ such that, for all i, an equational theory for $\mathfrak{A}_i$ and for the class $\mathfrak{A}_i \cap \mathfrak{F}$ of all finite semigroups in $\mathfrak{A}_i$ is undecidable while an equational theory for $\mathfrak{B}_i$ and for the class $\mathfrak{B}_i \cap \mathfrak{F}$ of all finite semigroups in $\mathfrak{B}_i$ is decidable. An infinite sequence of finitely based semigroup varieties $\mathfrak{A}_{\text{1}} \supset \mathfrak{B}_i \supset \mathfrak{A}_{\text{2}} \supset \mathfrak{B}_{\text{2}} \supset ...$ is constructed so that, for all i, an equational theory for $\mathfrak{B}_i$ and for the class $\mathfrak{B}_i \cap \mathfrak{F}$ of all finite semigroups in $\mathfrak{B}_i$ is decidable whicle an equational theory for $\mathfrak{A}_i$ and for the class $\mathfrak{A}_i \cap \mathfrak{F}$ of all finite semigroups in $\mathfrak{A}_i$ is not.

Keywords:
本文献已被 SpringerLink 等数据库收录！