A Remark on n-absorbing Ideals of Principal Ideal Domains

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Authors

  • 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 = p1r1 p2r2 p3r3 ...pkrk where k ≤ n and r1 + r2 + r3 + ... + rk ≤ n.