ASSOCIATED PRIMES OVER ORE EXTENSION RINGS

Author:

ANNIN SCOTT1

Affiliation:

1. Mathematics Department, California State University, 800 N. State College Blvd., Fullerton, CA 92831, USA

Abstract

The study of the prime ideals in Ore extension rings R[x,σ,δ] has attracted a lot of attention in recent years and has proven to be a challenging undertaking ([5], [7], [12], et al.). The present article makes a contribution to this study for the associated prime ideals. More precisely, we aim to describe how the associated primes of an R-module MR behave under passage to the polynomial module M[x] over an Ore extension R[x,σ,δ]. If we impose natural σ-compatibility and δ-compatibility assumptions on the module MR (see Sec. 2 below), we can describe all associated primes of the R[x,σ,δ]-module M[x] in terms of the associated primes of MR in a very straightforward way. This result generalizes the author's recent work [1] on skew polynomial rings.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Reference12 articles.

1. ASSOCIATED PRIMES OVER SKEW POLYNOMIAL RINGS

2. Associated primes of principal ideals

3. Associated primes in commutative polynomial rings

4. Mem. Amer. Math. Soc.;Goodearl K.,1994

5. London Mathematical Society Student Texts;Goodearl K.,1989

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