본문 바로가기
KERD
논문KCI 등재

On a special class of matrix rings

Arnab Bhattacharjee
대한수학회 (The Korean Mathematical Society)|2024.04|대한수학회논문집 (Communications of the KMS)|제39권 제2호|pp. 267-278|DOI 10.4134/CKMS.c220356

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

IFP ringsymmetric ringreversible ringreflexive ringStaircase matrix ring
주제분류수학

초록

In this paper, we continue to explore an idea presented in \cite{bhatt2020} and introduce a new class of matrix rings called \emph{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.

Abstract

In this paper, we continue to explore an idea presented in \cite{bhatt2020} and introduce a new class of matrix rings called \emph{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.

참고문헌 (15)

  1. N. Agayev, "Extended Armendariz rings", Algebras Groups Geom, 26(4), pp.343~354 (2009)
  2. H. E. Bell, "Near-rings in which each element is a power of itself", Bull. Austral. Math. Soc, 2(3), pp.363~368 (1970)[DOI]
  3. A. Bhattacharjee, "Ring endomorphisms satisfying the central reversible property", Proc. Indian Acad. Sci. Math. Sci, 130(1), pp.22~ (2020)[DOI]
  4. U. S. Chakraborty, "On some classes of reflexive rings", Asian-Eur. J. Math, 8(1), pp.15~ (2015)[DOI]
  5. W. Chen, "Central reversible rings", Acta Math. Sinica(Chinese Ser. ), 60(6), pp.1057~1064 (2017)
  6. P. M. Cohn, "Reversible rings", Bull. London Math. Soc, 31(6), pp.641~648 (1999)[DOI]
  7. C. Huh, "Basic examples and extensions of symmetric rings", J. Pure Appl. Algebra, 202(1-3), pp.154~167 (2005)[DOI]
  8. C. Huh, "Armendariz rings and semicommutative rings", Comm. Algebra, 30(2), pp.751~761 (2002)[DOI]
  9. D. W. Jung, "On properties related to reversible rings", Bull. Korean Math. Soc, 52(1), pp.247~261 (2015)[DOI]
  10. G. Kafkas-Demirci, "Generalized symmetric rings", Algebra Discrete Math, 12(2), pp.72~84 (2011)
  11. N. K. Kim, "Extensions of reversible rings", J. Pure Appl. Algebra, 185(1-3), pp.207~223 (2003)[DOI]
  12. T. K. Kwak, "Reflexive property of rings", Comm. Algebra, 40(4), pp.1576~1594 (2012)[DOI]
  13. J. Lambek, "On the representation of modules by sheaves of factor modules", Canad. Math. Bull, 14(3), pp.359~368 (1971)[DOI]
  14. G. Mason, "Reflexive ideals", Comm. Algebra, 9(17), pp.1709~1724 (1981)[DOI]
  15. T. ¨ Ozen, "On a class of semicommutative rings", Kyungpook Math. J, 51(3), pp.283~291 (2011)[DOI]

관련 논문AI추천

On commutativity of regular products이양, 곽태근, 서연숙대한수학회 · 대한수학회보2018 · 제55권 제6호Rings with many regular elementsEbrahim Nasibi, Nahid Ashrafi대한수학회 · 대한수학회논문집2017 · 제32권 제2호On reversibility related to idempotents이양, 류성주, 박상원, 성효진, 윤상조, 이창익, 정다운대한수학회 · 대한수학회보2019 · 제56권 제4호Quasipolar matrix rings over local ringsJian Cui, Xiaobin Yin대한수학회 · 대한수학회보2014 · 제51권 제3호Sums of tripotent and nilpotent matricesHuanyin Chen, Marjan Sheibani Abdolyousefi대한수학회 · 대한수학회보2018 · 제55권 제3호2×2 invertible matrices over weakly stable ringsHuanyin Chen대한수학회 · 대한수학회지2009 · 제46권 제2호

이 간행물의 다른 논문 (19건)

A survey of lengths of linear groups with respect to certain generating setsNguyen Thi Thai Happ. 279-302Cohen-Macaulay dimension for complexesFatemeh Mohammadi Aghjeh Mashhadpp. 303-311A weaker notion of the finite factorization propertyShihan Kanungo, Henry Jiang, Hwisoo Kimpp. 313-329NONLINEAR MIXED ∗-JORDAN TYPE n-DERIVATIONS ON ∗-ALGEBRASAbbas Hussain Shikeh, Mohammad Aslam Siddeeque, Raof Ahmad Bhatpp. 331-343On the number of equivalence classes of bi-partitions arising from the color change김병찬pp. 345-352
원문 보기