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Zero-divisors of Semigroup Modules

Peyman Nasehpour
경북대학교 자연과학대학 수학과|2011.03|Kyungpook Mathematical Journal|제51권 제1호|pp. 37-42

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참고문헌

키워드

Property (A)Dedekind-Mertens LemmaSemigroup modulesFew zero-divisorsMcCoy's propertyPrimal modules
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초록

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

Abstract

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

참고문헌 (22)

  1. J. T. Arnold, "On the content of polynomials", Proc. Amer. Math. Soc, 40, pp.556~562 (1970)
  2. 강병균, "CONTENT FORMULAS FOR POLYNOMIALS AND POWER SERIES AND COMPLETE INTEGRAL CLOSURE", JOURNAL OF ALGEBRA, 181(1), pp.82~94
  3. W. Bruns, "The Dedekind-Mertens formula and determinantal rings", Proc. Amer. Math. Soc, 127, pp.657~663 (1999)
  4. W. Bruns, "Cohen-Macaulay Rings, revised edn" (1998)
  5. J. Dauns, "Primal modules", Comm. Algebra, 25, pp.2409~2435 (1997)
  6. R. Gilmer, "Multiplicative Ideal Theory" (1972), Marcel Dekker
  7. R. Gilmer, "Commutative Semigroup Rings" (1984), The University of Chicago Press
  8. R. Gilmer, "Zero divisors in power series rings", J. Reine Angew. Math, 278, pp.145~164 (1975)
  9. W. Heinzer, "The Dedekind-Mertens Lemma and the content of poly-nomials", Proc. Amer. Math. Soc, 126, pp.1305~1309 (1998)
  10. J. A. Huckaba, "Commutative Rings with Zero Divisors" (1988), Marcel Dekker
  11. J. A. Huckaba, "Annihilation of ideals in commutative rings", Pac. J. Math, 83, pp.375~379 (1979)
  12. B. D. Janeway, "Zero divisors in commutative semigroup rings", Comm. Algebra, 12, pp.1877~1887 (1984)
  13. I. Kaplansky, "Commutative Rings" (1970), Allyn and Bacon
  14. N. H. McCoy, "Remarks on divisors of zero", Amer. Math. Monthly, 49, pp.286~295 (1942)
  15. P. Nasehpour, "Content algebras over commutative rings with zero divisors, arXiv:0807.1835v3, preprint", ~
  16. D. G. Northcott, "A generalization of a theorem on the content of polynomials", Proc. Cambridge Phil. Soc, 55, pp.282~288 (1959)
  17. P. Nasehpour, "Modules having few zero-divisors", Comm. Algebra
  18. P. Nasehpour, "M-cancellation Ideals", Kyungpook Math. J, 40, pp.259~263 (2000)
  19. J. Ohm, "Content modules and algebras", Math. Scand, 31, pp.49~68 (1972)
  20. D. E. Rush, "Content algebras", Canad. Math. Bull, 21(3), pp.329~334 (1978)
  21. H. Tsang, "Gauss' lemma", 박사, pp.1965
  22. O. Zariski, "Commutative Algebra, Vol. I" (1958), Van Nostrand

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