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 press

Authors:

S.J. Gogoi

Saurav J. Gogoi

Department of Mathematics
Gauhati University
Guwahati-14, Assam, India

email: sauravjyoti53@gmail.com

0009-0008-9702-8937

H.K. Saikia

Helen K. Saikia

Department of Mathematics
Gauhati University
Guwahati-14, Assam, India

email: hsaikia@yahoo.com

0000-0003-1971-9472

Title:

A note on tri-clean rings

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2024-08-27 , Revised: 2024-10-31 , Accepted: 2024-10-31 , Available online: 2025-05-29 , https://doi.org/10.7151/dmgaa.1481

Abstract:

We introduce a new class of rings, in which elements are sum of units and tripotents. This class of rings is called tri-clean ($T$-clean) rings which is a generalized structure of clean rings and invo tri-clean rings. We derive several properties of $T$-clean rings. We show that if an element $a$ is $T$-clean in a corner ring $eRe$ for some idempotent $e$ then it is also a $T$-clean element in $R$. If $2$ is an unit in $R$ then $R$ is a $T$-clean ring if and only if $\frac{R}{I}$ is a $T$-clean ring for every nil ideal $I$ of $R$. We also prove that all the upper triangular matrix rings over $T$-clean ring is a $T$-clean ring.

Keywords:

clean rings, $T$-clean rings, tripotents, lifting tripotents, ideal extension

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