Department of Mathematics M. J. College, Jalgaon - 425 002
,IN
Keywords:
Principal Ideal Domain, n-Absorbing Ideal, n-Absorbing Domain.
Abstract
Let R be a commutative ring with identity 1 ≠0. General-izing the notion of prime ideals in R, Anderson and Badawi introduced the notion of n-absorbing ideals in R. We introduce the notion of n- absorbing domains which is a generalization of an integral domain. We investigate all n-absorbing ideals in a PID R and hence prove that Zm is an n-absorbing domain if and only if m = p1r1p2r2p3r3 ...pkrk where k ≤ n and r1 + r2 + r3 + ... + rk ≤ n.