ScholarLens Back to search
1993•Journal of the Australian Mathematical Society Series A Pure Mathematics and StatisticsOpen access

Ideal extensions of Γ-rings

A. J. M. Snyders, Stefan Veldsman

Open full text 1 citations

Abstract

Abstract Given Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.

Open-access reader

About this research paper

What this paper is about

Abstract Given Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract Given Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.

Key concepts: Mathematics, Ideal (ethics), Extension (predicate logic), Ring (chemistry), Pure mathematics, Principal ideal ring, Maximal ideal, Simple ring

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Ideal extensions of Γ-rings — Research Paper | ScholarLens