Theories of first order of integer semigroup rings
type: Item
instance of: scholarly article
title: Theories of first order of integer semigroup rings
zbMATH Open document ID: 0846.20061
author: V. A. Tyukov
published in: Russian Mathematics
publication date: 1996-05-12T00:00:00Z
review text: The aim of the paper is to start studying the first order theories of semigroup rings. From the author's commentary: ``In the first section we consider integer semigroup rings of free semigroups of no more than countable rank and of cyclic groups. We establish criteria of elementary equivalence of such rings. In the second section we consider integer semigroup rings of free semigroups with unit of arbitrary rank and cyclic semigroups. We describe decidable theories of such rings in the frames of the scheme-alternative hierarchy, which was defined in [\textit{Yu. M. Vazhenin}, Algebra Logika 26, No. 4, 419-434 (1987; Zbl 0647.03006)]''.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 03C07
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20A15
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20M25
zbMATH DE Number: 857530
zbMATH Keywords: first order theories of semigroup rings
zbMATH Keywords: integer semigroup rings
zbMATH Keywords: free semigroups
zbMATH Keywords: elementary equivalence
zbMATH Keywords: decidable theories
reviewed by: Josif S. Ponizovskii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 857530