1
$\begingroup$

I want to know that in the commutative rings, the definition of the primary module is coincide with the definition of the primary ring? And where i can find it? The primary ring is a ring when ab=0, so a=0 or a power of b is zero and a primary module is a module with only one associated prime.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

I'm not quite sure of what you are asking. I guess that what you want to check is that if $R$ is a primary ring, then it is primary as an $R$-module. In this case $R$ being primary means that if $I$ is the ideal of nilpotent elements, then $R/I$ is an integral domain. It follows that $I$ is the only associated prime and hence you get the definition you want.

I'm using Ernst Kunz Introduction to Commutative Algebra and Algebraic Geometry to get my definitions here.

Improve this answer
$\endgroup$

Not the answer you're looking for? Browse other questions tagged .