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Some examples of quasi-Armendariz rings

Ebrahim Hashemi
대한수학회 (The Korean Mathematical Society)|2007.08|대한수학회보 (Bulletin of the KMS)|제44권 제3호|pp. 407-414

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Abstract

In [12], McCoy proved that ifR is a commutative ring, thenwhenever g(x) is a zero-divisor inR[x], there exists a nonzeroc 2 R suchthat cg(x) = 0. In this paper, rst we extend this result to monoid rings.Then for a monoid M , we give some examples of M -quasi-Armendarizrings which are a generalization of quasi-Armendariz rings. Every re-duced ring is M -quasi-Armendariz for any unique product monoid Mand any strictly totally ordered monoid ( M; ). AlsoT4(R) is M -quasi-Armendariz when R is reduced and M -Armendariz.

참고문헌 (17)

  1. Armendariz, "A note on extensions of Baer and p" (1974)
  2. D. Anderson, "Armendariz rings and Gaussian rings", 73, pp.14~17 (1997)
  3. G. F. Birkenmeier, "Triangular matrix representations of ring extensions", 265(2), pp.103~122 (2003)
  4. G. F Birkenmeier, "Polynomial extensions of Baer and quasi-Baer rings", 159(1), pp.25~42 (2001)
  5. Y. Hirano, "On annihilator ideals of a polynomial ring over a noncommutative ring", 168(1), pp.45~52 (2002)
  6. Y. Hirano, "On ordered monoid rings over a quasi-Baer ring", 29(5), pp.2089~2095 (2001)
  7. C. Y. Hong, "On skew Armendariz rings", 31(1), pp.103~122 (2003)
  8. C. Huh, "Armendariz rings and semicommutative rings", 30(2), pp.751~761 (2002)
  9. N. H Kim, "Armendariz rings and reduced rings", 223(2), pp.477~488 (2000)
  10. J. Krempa, "Some examples of reduced rings", 3(4), pp.289~300 (1996)
  11. T. K. Lee, "On Armendariz rings", 29(3), pp.583~593 (2003)
  12. McCoy, "Remarks on divisors of zero", pp.~49 (1942)
  13. Marcel Dekker, "Monographs and Textbooks in Pure and Applied Math-ematics" (1991), Inc
  14. Passman, "The Algebraic structure of group rings" (1977)
  15. M. B. Rege, "Armendariz rings", 73(1), pp.14~17 (1997)
  16. Pure Appl, "Noetherian rings of generalized power series", pp.~79 (1992)
  17. "Armendariz rings relative to a monoid", 33(3), pp.649~661 (2005)

관련 논문AI추천

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