On Factorization in Modules

Abstract

In two articles, Anderson and Valdes-Leon generalized the theory of factorization in integral domains to commutative rings with zero divisors and to modules. Here we investigate some factorization properties in modules and state a result that relates factorization properties of an R-module, M, to the factorization properties of M as an (R/Ann(M))-module. Furthermore, we will investigate when a polynomial module, M[x], has the bounded factorization property, assuming that M has this property.

Key Words:

• Bounded factorization module
• Irreducible element
• Présimplifiable
• Primitive element
• Unique factorization module
• Weakly présimplifiable

2000 Mathematics Subject Classification:

• 13A05
• 13C99
• 13F20
• 13E99

ACKNOWLEDGMENT

The authors would like to thank the referee for reading the article so carefully and for comments made on the article.

Notes

Communicated by J. Zhang.