Yıl 2018, Cilt 5, Sayı 3, Sayfalar 117 - 127 2018-10-08
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## Characterization of $2\times 2$ nil-clean matrices over integral domains

#### Kota Nagalakshmi Rajeswari [1] , Umesh Gupta [2]

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Let $R$ be any ring with identity. An element $a \in R$ is called nil-clean, if $a=e+n$ where $e$ is an idempotent element and $n$ is a nil-potent element. In this paper we give necessary and sufficient conditions for a $2\times 2$ matrix over an integral domain $R$ to be nil-clean.
Nil-clean matrix, Idempotent matrix, Nil-potent matrix, Diophantine equation
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Birincil Dil en Mühendislik Makaleler Orcid: 0000-0002-7722-2491Yazar: Kota Nagalakshmi Rajeswari (Sorumlu Yazar) Orcid: 0000-0001-7732-5768Yazar: Umesh Gupta
 Bibtex @araştırma makalesi { jacodesmath451229, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {Yıldız Teknik Üniversitesi}, year = {2018}, volume = {5}, pages = {117 - 127}, doi = {10.13069/jacodesmath.451229}, title = {Characterization of \$2\\times 2\$ nil-clean matrices over integral domains}, key = {cite}, author = {Gupta, Umesh and Rajeswari, Kota Nagalakshmi} } APA Rajeswari, K , Gupta, U . (2018). Characterization of $2\times 2$ nil-clean matrices over integral domains. Journal of Algebra Combinatorics Discrete Structures and Applications, 5 (3), 117-127. DOI: 10.13069/jacodesmath.451229 MLA Rajeswari, K , Gupta, U . "Characterization of $2\times 2$ nil-clean matrices over integral domains". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018): 117-127 Chicago Rajeswari, K , Gupta, U . "Characterization of $2\times 2$ nil-clean matrices over integral domains". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018): 117-127 RIS TY - JOUR T1 - Characterization of $2\times 2$ nil-clean matrices over integral domains AU - Kota Nagalakshmi Rajeswari , Umesh Gupta Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.451229 DO - 10.13069/jacodesmath.451229 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 117 EP - 127 VL - 5 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.451229 UR - http://dx.doi.org/10.13069/jacodesmath.451229 Y2 - 2018 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Characterization of $2\times 2$ nil-clean matrices over integral domains %A Kota Nagalakshmi Rajeswari , Umesh Gupta %T Characterization of $2\times 2$ nil-clean matrices over integral domains %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 3 %R doi: 10.13069/jacodesmath.451229 %U 10.13069/jacodesmath.451229 ISNAD Rajeswari, Kota Nagalakshmi , Gupta, Umesh . "Characterization of $2\times 2$ nil-clean matrices over integral domains". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 3 (Ekim 2018): 117-127. http://dx.doi.org/10.13069/jacodesmath.451229