대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권2호
  • /
  • Pages.267-278
  • /
  • 2024
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON A SPECIAL CLASS OF MATRIX RINGS

  • Arnab Bhattacharjee (Department of Mathematics Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya)
  • 투고 : 2020.12.09
  • 심사 : 2023.03.30
  • 발행 : 2024.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we continue to explore an idea presented in [3] and introduce a new class of matrix rings called staircase matrix rings which has applications in noncommutative ring theory. We show that these rings preserve the notions of reduced, symmetric, reversible, IFP, reflexive, abelian rings, etc.

키워드

과제정보

The author wishes to thank Dr. U. S. Chakraborty for his valuable comments and suggestions.

참고문헌

  1. N. Agayev, A. Harmanci, and S. Halicioglu, Extended Armendariz rings, Algebras Groups Geom. 26 (2009), no. 4, 343-354. 
  2. H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), no. 3, 363-368. https://doi.org/10.1017/S0004972700042052 
  3. A. Bhattacharjee and U. S. Chakraborty, Ring endomorphisms satisfying the central reversible property, Proc. Indian Acad. Sci. Math. Sci. 130 (2020), no. 1, Paper No. 12, 22 pp. https://doi.org/10.1007/s12044-019-0548-y 
  4. U. S. Chakraborty, On some classes of reflexive rings, Asian-Eur. J. Math. 8 (2015), no. 1, 1550003, 15 pp. https://doi.org/10.1142/S1793557115500035 
  5. W. Chen, Central reversible rings, Acta Math. Sinica (Chinese Ser.) 60 (2017), no. 6, 1057-1064. 
  6. P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), no. 6, 641-648. https://doi.org/10.1112/S0024609399006116 
  7. C. Huh, H. K. Kim, N. K. Kim, and Y. Lee, Basic examples and extensions of symmetric rings, J. Pure Appl. Algebra 202 (2005), no. 1-3, 154-167. https://doi.org/10.1016/j.jpaa.2005.01.009 
  8. C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. https://doi.org/10.1081/AGB-120013179 
  9. D. W. Jung, N. K. Kim, Y. Lee, and S. J. Ryu, On properties related to reversible rings, Bull. Korean Math. Soc. 52 (2015), no. 1, 247-261. https://doi.org/10.4134/BKMS.2015.52.1.247 
  10. G. Kafkas-Demirci, B. Ungor, S. Halicioglu, and A. Harmanci, Generalized symmetric rings, Algebra Discrete Math. 12 (2011), no. 2, 72-84. 
  11. N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207-223. https://doi.org/10.1016/S0022-4049(03)00109-9 
  12. T. K. Kwak and Y. Lee, Reflexive property of rings, Comm. Algebra 40 (2012), no. 4, 1576-1594. https://doi.org/10.1080/00927872.2011.554474 
  13. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), no. 3, 359-368. https://doi.org/10.4153/CMB-1971-065-1 
  14. G. Mason, Reflexive ideals, Comm. Algebra 9 (1981), no. 17, 1709-1724. https://doi.org/10.1080/00927878108822678 
  15. T. Ozen, N. Agayev, and A. Harmanci, On a class of semicommutative rings, Kyungpook Math. J. 51 (2011), no. 3, 283-291. https://doi.org/10.5666/KMJ.2011.51.3.283