Yıl 2017, Cilt 22, Sayı 22, Sayfalar 147 - 169 2017-07-11

Idempotents and Units of Matrix Rings over Polynomial Rings

Pramod Kanwar [1] , Meenu Khatkar [2] , R. K. Sharma [3]

151 91

The aim of this paper is to study idempotents and units in certain matrix rings over polynomial rings. More precisely, the conditions under which an element in $M_2(\mathbb{Z}_p[x])$ for any prime $p$, an element in $M_2(\mathbb{Z}_{2p}[x])$ for any odd prime $p$, and an element in $M_2(\mathbb{Z}_{3p}[x])$ for any prime $p$ greater than 3 is an idempotent are obtained and these conditions are used to give the form of idempotents in these matrix rings. The form of elements in $M_2(\mathbb{Z}_2[x])$ and elements in $M_2(\mathbb{Z}_3[x])$ that are units is also given. It is observed that unit group of these rings behave differently from the unit groups of $M_2(\mathbb{Z}_2)$ and $M_2(\mathbb{Z}_3)$.
 

Idempotent, unit
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Konular Matematik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Pramod Kanwar

Yazar: Meenu Khatkar

Yazar: R. K. Sharma

Bibtex @araştırma makalesi { ieja325941, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {22}, pages = {147 - 169}, doi = {10.24330/ieja.325941}, title = {Idempotents and Units of Matrix Rings over Polynomial Rings}, key = {cite}, author = {Sharma, R. K. and Kanwar, Pramod and Khatkar, Meenu} }
APA Kanwar, P , Khatkar, M , Sharma, R . (2017). Idempotents and Units of Matrix Rings over Polynomial Rings. International Electronic Journal of Algebra, 22 (22), 147-169. DOI: 10.24330/ieja.325941
MLA Kanwar, P , Khatkar, M , Sharma, R . "Idempotents and Units of Matrix Rings over Polynomial Rings". International Electronic Journal of Algebra 22 (2017): 147-169 <http://dergipark.gov.tr/ieja/issue/30344/325941>
Chicago Kanwar, P , Khatkar, M , Sharma, R . "Idempotents and Units of Matrix Rings over Polynomial Rings". International Electronic Journal of Algebra 22 (2017): 147-169
RIS TY - JOUR T1 - Idempotents and Units of Matrix Rings over Polynomial Rings AU - Pramod Kanwar , Meenu Khatkar , R. K. Sharma Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.325941 DO - 10.24330/ieja.325941 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 147 EP - 169 VL - 22 IS - 22 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.325941 UR - http://dx.doi.org/10.24330/ieja.325941 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra Idempotents and Units of Matrix Rings over Polynomial Rings %A Pramod Kanwar , Meenu Khatkar , R. K. Sharma %T Idempotents and Units of Matrix Rings over Polynomial Rings %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 22 %N 22 %R doi: 10.24330/ieja.325941 %U 10.24330/ieja.325941
ISNAD Kanwar, Pramod , Khatkar, Meenu , Sharma, R. K. . "Idempotents and Units of Matrix Rings over Polynomial Rings". International Electronic Journal of Algebra 22 / 22 (Temmuz 2017): 147-169. http://dx.doi.org/10.24330/ieja.325941