The asymptotic closure of an ideal relative to a module

Authors

  • Sylvia M. Foster
  • Johnny A. Johnson

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.379

Abstract

In this paper we introduce the concept of the asymptotic closure of an ideal of a commutative ring $ R $ with identity relative to a unitary $ R $-module $ M $. This work extends results from P. Samuel, M. Nagata, J. W. Petro and Sharp, Tiras, and Yassi. Our objectives in this paper are to establish the cancellation law for the asymptotic completion of an ideal relative to a finitely generated module and show that the integral closure of an ideal relative to a Noetherian module $ M $ coincides with the asymptotic closure of the ideal relative to the Noetherian module $ M $.

Author Biography

Sylvia M. Foster

Department of Mathematics, University of Houston, Houston, Texas 77204-3476, U.S.A.

Published

2001-09-30

How to Cite

Foster, S. M., & Johnson, J. A. (2001). The asymptotic closure of an ideal relative to a module. Tamkang Journal of Mathematics, 32(3), 231-235. https://doi.org/10.5556/j.tkjm.32.2001.379

Issue

Section

Papers