DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume


Authors:

A.B. Singh

Amit B. Singh

Jamia Hamdard (Deemed to be University)
New Delhi 110 062, India

email: amit.bhooshan84@gmail.com

S. Kumar

Susheel Kumar

Deshbandhu College (University of Delhi)
New Delhi 110 019, India

email: skahlawatt@gmail.com

Title:

Super strongly clean group rings

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 135-140

Received: 2021-07-29 , Revised: 2021-10-27 , Accepted: 2021-11-07 , Available online: 2023-01-12 , https://doi.org/10.7151/dmgaa.1421

Abstract:

In this paper, we study super strongly clean group rings for different classes of rings and groups. Mainly, we prove the following results:
  1. Let $R$ be a ring with $2\in J(R)$ and $G$ be a locally finite $2$-group. Then the group ring $RG$ is super strongly clean if and only if $R$ is super strongly clean.
  2. If $R$ is a local ring with $p\in J(R)$ and $G$ is a locally finite $p$-group, then the group ring $RG$ is super strongly clean.
  3. If $R$ is an abelian exchange ring with $2\in J(R)$ and $G$ is a locally finite $2$-group, then the group ring $RG$ is super strongly clean.

Keywords:

super strongly clean ring, clean ring, group ring, locally finite p-group

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