Let $A\to R$ be a ring homomorphism between two commutative rings with unity. I want to know what is it meant by conductor of a map $A\to R$. Is it the annhilator in $A$ of the $R$-module $R/A$?
In Eisenbud (Commutative algebra with a view towards Algebraic Geometry) page 272 this is defined for the normalisation map of a Noetherian domain. For an arbitrary map is it defined the above way?
Also where can I found the conductor ideal of such map (in commutative algebra context).
Thank you in advance.