Semigroup rings which are finite direct products of Galois rings
type: Item
instance of: scholarly article
title: Semigroup rings which are finite direct products of Galois rings
zbMATH Open document ID: 0935.20058
published in: Semigroup Forum
publication date: 2000-02-07T00:00:00Z
review text: Let \(R\) be an associative ring, and let \(p\) be a prime. A polynomial \(f\in R[x]\) is said to be irreducible modulo \(p\) if so is the image of \(f\) under the natural ring homomorphism \(R[x]\to R[x]/pR[x]\). A Galois ring is a ring of the form \((\mathbb{Z}/p^m\mathbb{Z})[x]/(f(x))\), where \(p\) is a prime, and \(f(x)\in(\mathbb{Z}/p^m\mathbb{Z})[x]\) is a monic polynomial that is irreducible modulo \(p\). The author gives a full description of the commutative semigroup rings in the title.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 13M10
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 1356250
zbMATH Keywords: Galois rings
zbMATH Keywords: irreducible polynomials
zbMATH Keywords: commutative semigroup rings
zbMATH Keywords: polynomial rings
author: A. V. Kelarev
reviewed by: Josif S. Ponizovskii
MaRDI profile type: Publication
full work available at URL: s002339900065
OpenAlex ID: W2043962226
DOI: 10.1007/S002339900065
description: scientific article; zbMATH DE number 1356250