Certain Clean Decompositions for Matrices over Local Rings

被引：0
作者：
Kurtulmaz, Yosum [1 ]
Kose, Handan [2 ]
Chen, Huanyin [3 ]
机构：
[1] Bilkent Univ, Dept Math, Ankara, Turkiye
[2] Ahi Evran Univ, Dept Math, Kirsehir, Turkiye
[3] Fuzhou Univ Int Studies & Trade, Sch Big Data, Fuzhou 350202, Peoples R China
来源：
KYUNGPOOK MATHEMATICAL JOURNAL | 2023年 / 63卷 / 04期
关键词：
Strongly clean matrix; Strongly rad-clean matrix; Local ring; Power-series; SUM;
D O I：
10.5666/KMJ.2023.63.4.561
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An element a E R is strongly rad-clean provided that there exists an idempotent e E R such that a -e E U(R), ae = ea and eae E J(eRe). In this article, we completely determine when a 2 x 2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.
引用
收藏
页码：561 / 569
页数：9
相关论文
共 50 条
[21]   Enumeration of some matrices and free linear codes over commutative finite local rings [J].
Sirisuk, Siripong .
SPECIAL MATRICES, 2022, 10 (01) :109-116
[22]   On *-clean group rings over finite fields [J].
Han, Dongchun ;
Zhang, Hanbin .
FINITE FIELDS AND THEIR APPLICATIONS, 2021, 73
[23]   On Modules over Local Rings [J].
Erdogan, Fatma Ozen ;
Ciftci, Suleyman ;
Akpinar, Atilla .
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2016, 24 (01) :217-230
[24]   On a certain functional identity involving inverses in division rings and local rings [J].
Cezayirlioglu, Nefise ;
Demir, Cagri .
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025, 24 (09)
[25]   CERTAIN ADDITIVE DECOMPOSITIONS IN A NONCOMMUTATIVE RING [J].
Chen, Huanyin ;
Sheibani, Marjan ;
Bahmani, Rahman .
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2022, 72 (04) :1217-1226
[26]   UNITARY GROUPS OVER LOCAL RINGS [J].
Cruickshank, J. ;
Herman, A. ;
Quinlan, R. ;
Szechtman, F. .
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (02)
[27]   Projective covers over local rings [J].
Sofia Ercolanoni ;
Alberto Facchini .
Annali di Matematica Pura ed Applicata (1923 -), 2021, 200 :2631-2644
[28]   Stable cohomology over local rings [J].
Avramov, Luchezar L. ;
Veliche, Oana .
ADVANCES IN MATHEMATICS, 2007, 213 (01) :93-139
[29]   Projective covers over local rings [J].
Ercolanoni, Sofia ;
Facchini, Alberto .
ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (06) :2631-2644
[30]   Reducibility and irreducibility of monomial matrices over commutative rings [J].
Bondarenko, Vitaliy M. ;
Bortos, Maria Yu. ;
Dinis, Ruslana F. ;
Tylyshchak, Alexander A. .
ALGEBRA & DISCRETE MATHEMATICS, 2013, 16 (02) :171-187
12345