Group rings with annihilator conditions

A ring R is called left (Kasch) dual if every (maximal) left ideal of R is a left annihilator. R is left CF if every left ideal of R is the left annihilator of a finite number of elements of R . Let RG be the group ring of a group G over a ring R . It is proved that RG is a left Kasch ring if and on...

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Bibliographic Details
Published in:Acta mathematica Hungarica Vol. 156; no. 1; pp. 38 - 46
Main Author: Shen, L.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.10.2018
Springer Nature B.V
Subjects:
Mathematics
Mathematics and Statistics
Rings (mathematics)
CF ring
dual ring
16S34
perfect duality
group ring
Kasch ring
16D25
ISSN:0236-5294, 1588-2632
Online Access:Get full text
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Summary:A ring R is called left (Kasch) dual if every (maximal) left ideal of R is a left annihilator. R is left CF if every left ideal of R is the left annihilator of a finite number of elements of R . Let RG be the group ring of a group G over a ring R . It is proved that RG is a left Kasch ring if and only if R is left Kasch and G is finite. Characterizations of left dual (left CF ) group rings are also discussed in this article.
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ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-018-0860-5