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IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS

Yıl 2020, , 1 - 12, 07.01.2020
https://doi.org/10.24330/ieja.662942

Öz

We determine the forms of the nontrivial idempotents in the ring of $2\times 2$ matrices over the polynomial rings $\mathbb{Z}_{pq}[x]$ and $\mathbb{Z}_{p^2}[x]$, where $p$ and $q$ are any primes. Any such idempotent in the stated rings will be of a form in our list. Our work generalizes the results of Kanwar, Khatkar and Sharma (2017) who identified the forms of idempotents in $M_2(\mathbb{Z}_{2p}[x])$ and $M_2(\mathbb{Z}_{3p}[x])$.

Kaynakça

  • P. N. Anh, G. F. Birkenmeier and L. van Wyk, Idempotents and structures of rings, Linear Multilinear Algebra, 64(10) (2016), 2002-2029.
  • D. M. Burton, Elementary Number Theory, 6th Edition, Tata McGraw-Hill Education Pvt. Ltd., 2006.
  • M. Henriksen, Two classes of rings generated by their units, J. Algebra, 31 (1974), 182-193.
  • T. W. Hungerford, Abstract Algebra: An Introduction, 3rd Edition, Cengage Learning, 2012.
  • P. Kanwar, M. Khatkar and R. K. Sharma, Idempotents and units of matrix rings over polynomial rings, Int. Electron. J. Algebra, 22 (2017), 147-169.
  • P. Kanwar, A. Leroy and J. Matczuk, Idempotents in ring extensions, J. Alge- bra, 389 (2013), 128-136.
  • E. D. Nering, Linear Algebra and Matrix Theory, 2nd Edition, John Wiley & Sons Inc., 1970.
  • W. K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J., 46(2) (2004), 227-236.
  • A. K. Srivastava, Additive representations of elements in rings: a survey, in Algebra and its Applications, Springer Proc. Math. Stat., Springer, Singapore, 174 (2016), 59-73.
Yıl 2020, , 1 - 12, 07.01.2020
https://doi.org/10.24330/ieja.662942

Öz

Kaynakça

  • P. N. Anh, G. F. Birkenmeier and L. van Wyk, Idempotents and structures of rings, Linear Multilinear Algebra, 64(10) (2016), 2002-2029.
  • D. M. Burton, Elementary Number Theory, 6th Edition, Tata McGraw-Hill Education Pvt. Ltd., 2006.
  • M. Henriksen, Two classes of rings generated by their units, J. Algebra, 31 (1974), 182-193.
  • T. W. Hungerford, Abstract Algebra: An Introduction, 3rd Edition, Cengage Learning, 2012.
  • P. Kanwar, M. Khatkar and R. K. Sharma, Idempotents and units of matrix rings over polynomial rings, Int. Electron. J. Algebra, 22 (2017), 147-169.
  • P. Kanwar, A. Leroy and J. Matczuk, Idempotents in ring extensions, J. Alge- bra, 389 (2013), 128-136.
  • E. D. Nering, Linear Algebra and Matrix Theory, 2nd Edition, John Wiley & Sons Inc., 1970.
  • W. K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J., 46(2) (2004), 227-236.
  • A. K. Srivastava, Additive representations of elements in rings: a survey, in Algebra and its Applications, Springer Proc. Math. Stat., Springer, Singapore, 174 (2016), 59-73.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Jose Maria P. Balmaceda Bu kişi benim

Joanne Pauline P. Datu Bu kişi benim

Yayımlanma Tarihi 7 Ocak 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Balmaceda, J. M. P., & Datu, J. P. P. (2020). IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS. International Electronic Journal of Algebra, 27(27), 1-12. https://doi.org/10.24330/ieja.662942
AMA Balmaceda JMP, Datu JPP. IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS. IEJA. Ocak 2020;27(27):1-12. doi:10.24330/ieja.662942
Chicago Balmaceda, Jose Maria P., ve Joanne Pauline P. Datu. “IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS”. International Electronic Journal of Algebra 27, sy. 27 (Ocak 2020): 1-12. https://doi.org/10.24330/ieja.662942.
EndNote Balmaceda JMP, Datu JPP (01 Ocak 2020) IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS. International Electronic Journal of Algebra 27 27 1–12.
IEEE J. M. P. Balmaceda ve J. P. P. Datu, “IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS”, IEJA, c. 27, sy. 27, ss. 1–12, 2020, doi: 10.24330/ieja.662942.
ISNAD Balmaceda, Jose Maria P. - Datu, Joanne Pauline P. “IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS”. International Electronic Journal of Algebra 27/27 (Ocak 2020), 1-12. https://doi.org/10.24330/ieja.662942.
JAMA Balmaceda JMP, Datu JPP. IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS. IEJA. 2020;27:1–12.
MLA Balmaceda, Jose Maria P. ve Joanne Pauline P. Datu. “IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS”. International Electronic Journal of Algebra, c. 27, sy. 27, 2020, ss. 1-12, doi:10.24330/ieja.662942.
Vancouver Balmaceda JMP, Datu JPP. IDEMPOTENTS IN CERTAIN MATRIX RINGS OVER POLYNOMIAL RINGS. IEJA. 2020;27(27):1-12.