On semifir monoid rings
type: Item
instance of: scholarly article
title: On semifir monoid rings
zbMATH Open document ID: 0686.20043
DOI: 10.5565/PUBLMAT_33189_09
author: Ferran Cedó
published in: Publicacions Matemàtiques
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/41071
review text: A ring R is said to be a semifir if every finitely generated right ideal is free of unique rank. Let RM be the monoid ring of a non-trivial monoid M over the ring R. If R is a skew field and M is a directed union of free products of free groups and free monoids then it is known that RM is a semifir. W. Dicks has conjectured that the converse is also true. In this paper some necessary conditions on M for RM to be a semifir are given. Furthermore, the author constructs a monoid N (whose unit group is trivial) that satisfies all these conditions but it is not a directed union of free monoids. Therefore, if RN is a semifir, for some skew field R, then RN provides a counter-example to Dicks' conjecture. Unfortunately, whether or not RN is a semifir for some skew field R is not decided in the present paper.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S10
zbMATH DE Number: 4124005
zbMATH Keywords: monoid ring
zbMATH Keywords: skew field
zbMATH Keywords: directed union of free products of free groups and free monoids
zbMATH Keywords: semifir
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4124005