Ideal extensions of Γ-rings

A. J.M. Snyders; S. Veldsman

doi:10.1017/S1446788700031840

Ideal extensions of Γ-rings

A. J.M. Snyders, S. Veldsman

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	368-392
Number of pages	25
Journal	Journal of the Australian Mathematical Society
Volume	54
Issue number	3
DOIs	https://doi.org/10.1017/S1446788700031840
Publication status	Published - Jun 1993
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1017/S1446788700031840

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title = "Ideal extensions of Γ-rings",

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.",

author = "Snyders, {A. J.M.} and S. Veldsman",

year = "1993",

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AB - 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.

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Ideal extensions of Γ-rings

Abstract

ASJC Scopus subject areas

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