An element x in a ring R with unity is called almost clean if there exists some idempotent element e in R and a regular element u in R such that x = e + u. This article aims to show the existence of almost clean elements in a certain matrix ring over an integral domain R with unity and provide its characterizations.
REFERENCES
1.
W.K.
Nicholson
, Trans. AMS.
229
, 269
– 278
(1977
)2.
J.
Han
and W.K.
Nicholson
, Comm. Algebra
29
(6
), 2589
– 2595
(2001
).3.
W.K.
Nicholson
and Y.
Zhou
, Glasg. Math. J.
46
(2
), 227
– 236
(2004
).4.
5.
I.F.
Ambarsari
, S.
Irawati
, I.M.
Sulandra
, H.
Susanto
, and H.
Marubayashi
, AIP Conference Proceedings
2192
, pp 040001-1
- 040001-1
(2019
).6.
X.
Yang
and Y.
Zhou
, Linear Algebra and its Applications
425
, 119
– 129
(2007
).7.
H.
Chen
H, O.
Gurgun
and H.
Kose
, On Strongly Clean Triangular Matrix Ring
, (2013
), available at http://arxiv.org/abs/1307.7339v2.8.
G.
Tang
and Y.
Zhou
, Linear Algebra and its Applications
437
(10
), 2546
–2559
(2012
).9.
I.F.
Ambarsari
, S.
Irawati
, I.M.
Sulandra
, H.
Susanto
, A. Y. M
Chin
and H.
Marubayashi
, Journal of Physics Conference Series
1397
:012069
(2019
).10.
11.
A. Y. M.
Chin
and K.T
Qua
, Acta Mathematica Hungarica
132
(1
), 113
–116
(2011
).12.
A. J. J.
Diesl
, Algebra
383
, 197
– 211
(2013
).13.
M. F.M.
Al Habibi
, S.
Irawati
, H.
Susanto
, I.M.
Sulandra
, H.
Marubayashi
and I.F.
Ambarsari
, COMPUSOFT
8
(9
), 3410
–3414
(2019
)14.
W.W.
McGovern
, Communication in Algebra
31
(7
), 3295
–3304
(2003
).15.
W.C.
Brown
, Matrices over Commutative Rings
(Marcel Dekker, Inc
., New York
, 1993
), pp. 16
.
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.