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On Weakly
Présimplifiable
Group Rings
Omar A. Al-Mallah (1), M. Abu-Saleem (2),
Jebrel M. Habeb
(3)
and N. Jarboui
(4)
(1) Department
of Mathematics,
College of
Sciences, Al-Balqa
University,
Al-Salt 19117,
P.O. Box 206,
Jordan
Email address:
oamallah@bau.edu.jo
(2) Department of
Mathematics, College
of Sciences, Al-Balqa
University, Al-Salt
19117, P.O. Box 206,
Jordan
Email address:
m_abusaleem@bau.edu.jo
(3) [Corresponding
author] Department
of Mathematics,
College of Science,
Yarmouk University,
Irbid, Jordan
Email address:
jhabeb@yu.edu.jo
(4) Department of
Mathematics, Faculty
of Sciences of Sfax,
University of Sfax,
P.O. Box 1171, Safax
3038, Tunisia
Email address:
noomenjarboui@yahoo.fr
Doi :
https://doi.org/10.47013/15.4.15
Cited by :
Jordan J. Math &
Stat.,
15 (4B) (2022),
1015 - 1029
PDF
Received on:
Aug. 6, 2021;
Accepted
on: Dec. 23,
2021
Abstract. A
commutative ring
R with unity is
called weakly-présimplifiable
(resp.,
présimplifiable)
if for a, b ϵ R
with a = ba,
then either a =
0 or b is a
regular element
(that is, b is
not a
zero-divisor) in
R (resp., a = 0
or b is a unit
in R). Let R be
a commutative
ring with unity
and G be a
nontrivial
abelian group.
In this paper,
we give some
characterizations
for the group
ring R[G] to be
weakly
présimplifiable.
Furthermore, we
give a complete
description of
(weakly)
présimplifiable
circulant matrix
ring.
Keywords: Présimplifiable
ring,
indecomposable
ring, circulant
matrix ring.
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