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Extensions of extended symmetric rings

곽태근
대한수학회 (The Korean Mathematical Society)|2007.11|대한수학회보 (Bulletin of the KMS)|제44권 제4호|pp. 777-788

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Abstract

An endomorphism of a ring R is called right (left) symmet-ric if whenever abc = 0 for a;b;c2 R,ac (b) = 0 ((b)ac = 0). A ring Ris called right (left) -symmetricif there exists a right (left) symmetricendomorphism of R. The notion of an -symmetric ring is a general-ization of -rigid rings as well as an extension of symmetric rings. Westudy characterizations of-symmetric rings and their related propertiesincluding extensions. The relationship between -symmetric rings and(extended) Armendariz rings is also investigated, consequently severalknown results relating to -rigid and symmetric rings can be obtained ascorollaries of our results.

참고문헌 (13)

  1. "Armendariz rings and Gaussian rings", 26(7), pp.2265~2272 (1998)
  2. "Semigroups and rings whose zero products commute", 27(6), pp.2847~2852 (1999)
  3. "A note on extensions of Baer and P" (1974)
  4. "Reversible rings", 31(6), pp.641~648 (1999)
  5. "A note on zero commutative and duo rings" (1990), Okayama Univ
  6. "Ore extensions of Baer and p.p.-rings", 151(3), pp.215~226 (2000)
  7. "On skew Armendariz rings", 31(1), pp.103~122 (2003)
  8. "Extensions of generalized Armendariz rings", 13(2), pp.253~266 (2006)
  9. "Basic examples and extensions of symmetricrings", 202(1-3), pp.154~167 (2005)
  10. "Armendariz rings and semicommutative rings", 30(2), pp.751~761 (2002)
  11. "Some examples of reduced rings", 3(4), pp.289~300 (1996)
  12. "On the representation of modules by sheaves of factor modules" (1971)
  13. "Reversible and symmetric rings", 174(3), pp.311~318 (2002)

관련 논문AI추천

Skew power series extensions of $\alpha$-rigid p.p.-ringsAhmad Moussavi, Ebrahim Hashemi대한수학회 · 대한수학회보2004 · 제41권 제4호A Note on the Extended Sum of Radical Classes of RingsM. Aslam, M. Zulfiqar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제3호Generalizations of V-ringsXianmei Song, Xiaobin Yin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제3호The Cohn-Jordan extension and skew monoid rings over a quasi-Baer ringEbrahim Hashemi대한수학회 · 대한수학회논문집2006 · 제21권 제1호On Idempotent Reflexive RingsJin Yong Kim, Jong Uk Baik경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제4호Some examples of quasi-Armendariz ringsEbrahim Hashemi대한수학회 · 대한수학회보2007 · 제44권 제3호

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