Some Results on Finitely Laskerian Rings

Abstract

In Section 1 of this note we give an example of a strongly Laskerian domain D for which the polynomial ring D[x] admits a 2-generated ideal which does not admit a primary decomposition. In Section 2 of this note we prove that if R is a quasilocal ring with M as its unique maximal ideal such that R/Ann(M) is Artinian, then for any subring T of the polynomial ring R[x], each finitely generated proper ideal of T admits a primary decomposition.

Key Words:

• Finitely Laskerian pair
• Finitely Laskerian ring

1991 Mathematics Subject Classification:

• Primary 13A15
• Secondary 13B25

ACKNOWLEDGMENT

I am very much thankful to the referee for his/her suggestions and his/her help in converting my article into a TeX version.