On the comaximal (ideal) graph associated with amalgamated algebra

A → B be a ring homomorphism of the commutative rings A and B with identities.Let J be an ideal of B. The amalgamation of A with B along J with respect to f is a subring of A × B given by A f J := {(a, f (a) + j) | a ∈ A , j ∈ J}.In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A f J.In particular, we determine the Jacobson radical of A f J, characterize the diameter of the comaximal ideal graph of A f J, and investigate the clique number as well as the chromatic number of this graph.

Abstract licence: CC BY

16 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.