Remarks on α-strongly irreducible ideals

Abstract

In this article, we study α-irreducible and α-strongly irreducible ideals of a commutative ring. The relations between α-strongly irreducible ideals of a ring and α-strongly irreducible ideals of localization of the ring are also studied.

Keywords

α-irreducible / α-strongly irreducible / primary ideal / faithful module / multiplication module

References

[1] Azizi A. Strongly irreducible ideals. J Aust Math Soc, 2008, 84: 145-154

[2] Bernad B. Multiplication modules. J Algebra, 1981, 71: 174-178

[3] El-Bast Z A, Smith P F. Multiplication modules. Commun Algebra, 1988, 16(4): 755-779

[4] Heinzer W J, Ratliff L J, Rush D E. Strongly irreducible ideals. J Pure Appl Algebra, 2002, 166: 267-275

[5] Lam T Y. Lectures on Modules and Rings. New York: Springer-Verlag, 1999

[6] Lee D S, Lee H B. Some remarks on faithful multiplication modules. J Chungcheony Math Soc, 1993, 6: 131-137

[7] Lu X. α-Irreducible and α-strongly irreducible ideals of a ring. Southeast Asian Bulletin of Mathematics, 2008, 32: 299-303

[8] Nagata M. Local Rings. Interscience Tracts in Pure and Applied Math, 13. New York: Intersection, 1962

[9] Sharp R T. Steps in Commutative Algebra. Cambridge; Cambridge University Press, 1994

[10] Smith P F. Some remarks on multiplication modules. Arch Math, 1988, 50: 223-235

[11] Stenström Bo. Rings of Quotients, An Introduction to Methods of Ring Theory. Berlin, Heidelberg, New York: Springer-Verlag, 1975

[12] Zariski O, Samuel P. Commutative Algebra, Vol I. Princeton: D Van Nostrand Co, Inc, 1965

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg