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## Characterization of $2\times 2$ nil-clean matrices over integral domains

#### Kota Nagalakshmi RAJESWARİ [1] , Umesh GUPTA [2]

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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Primary Language en Engineering Articles Orcid: 0000-0002-7722-2491Author: Kota Nagalakshmi RAJESWARİ (Primary Author) Orcid: 0000-0001-7732-5768Author: Umesh GUPTA Publication Date : October 8, 2018
 Bibtex @research article { jacodesmath451229, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, 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 = {Rajeswari̇, Kota Nagalakshmi and Gupta, Umesh} } APA Rajeswari̇, 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 Rajeswari̇, 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 Rajeswari̇, 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 Rajeswari̇ , 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 - https://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 Rajeswari̇ , 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 Rajeswari̇, 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 (October 2018): 117-127 . https://doi.org/10.13069/jacodesmath.451229 AMA Rajeswari̇ K , Gupta U . Characterization of $2\times 2$ nil-clean matrices over integral domains. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(3): 117-127. Vancouver Rajeswari̇ K , Gupta U . Characterization of $2\times 2$ nil-clean matrices over integral domains. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(3): 117-127.

Authors of the Article
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[2]