Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring
type: Item
instance of: scholarly article
title: Finite completely primary rings in which the product of any two zero divisors of a ring is in its coefficient subring
zbMATH Open document ID: 0814.16016
DOI: 10.1155/S0161171294000670
author: Yousef Alkhamees
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/47161
review text: The paper deals with finite completely primary rings. On any Galois ring \(S\) of the form \(\text{GR}(p^ n,n)\) a construction of a new ring is given. It is proved that in any completely finite primary ring the product of any two zero-divisors is an element of its coefficient subring if and only if it is one of the rings given by the defined construction. It is proved that finite rings in which the product of any two zero divisors is a power of a fixed prime \(q\) are completely primary rings where either the set of zero divisors \(J\) has \(J^ 2 = 0\) or their coefficient subring is \(Z_{2^ n}\) with \(n = 2\) or 3. Finally, the enumeration of such rings is determined.
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 13M05
zbMATH DE Number: 650815
zbMATH Keywords: product of zero-divisors
zbMATH Keywords: finite completely primary rings
zbMATH Keywords: Galois ring
zbMATH Keywords: finite rings
reviewed by: Thomas Vougiouklis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 650815