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EXTENSIONS OF McCOY'S THEOREM

Published online by Cambridge University Press:  04 December 2009

CHAN YONG HONG ,
NAM KYUN KIM  and
YANG LEE
CHAN YONG HONG
Affiliation:
Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 131-701, Korea e-mail: hcy@khu.ac.kr
NAM KYUN KIM*
Affiliation:
College of Liberal Arts and Sciences, Hanbat National University, Daejeon 305-719, Korea e-mail: nkkim@hanbat.ac.kr
YANG LEE
Affiliation:
Department of Mathematics Education, Pusan National University, Pusan 609-735, Korea e-mail: ylee@pusan.ac.kr
*
*Corresponding author.
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Abstract

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McCoy proved that for a right ideal A of S = R[x1, . . ., xk] over a ring R, if rS(A) ≠ 0 then rR(A) ≠ 0. We extend the result to the Ore extensions, the skew monoid rings and the skew power series rings over non-commutative rings and so on.

Keywords

Primary: 16S3616N60Secondary: 13B2516W20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 155 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Fields, D. E., Zero divisors and nilpotent elements in power series rings, Proc. Amer. Math. Soc. 27 (1971), 427–433.CrossRefGoogle Scholar
2.Gilmer, R. and Parker, T., Zero divisors in power series rings, J. Reine Angew. Math. 278/279 (1975), 145–164.Google Scholar
3.Hirano, Y., On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52.CrossRefGoogle Scholar
4.McCoy, N. H., Remarks on divisors of zero, Amer. Math. Monthly 49 (1942), 286–295.CrossRefGoogle Scholar
5.McCoy, N. H., Annihilators in polynomial rings, Amer. Math. Monthly 64 (1957), 28–29.Google Scholar
6.Nielsen, P. P., Semi-commutativity and the McCoy condition, J. Algebra 298 (2006), 134–141.CrossRefGoogle Scholar
7.Okninski, J., Semigroup algebras (Marcel Dekker, New York, 1991).Google Scholar
8.Passmann, D. S., The algebraic structure of group rings (John Wiley & Sons, New York, 1977).Google Scholar
9.Weiner, L., Concerning a theorem of McCoy, Amer. Math. Monthly 59 (1952), 336–337.Google Scholar