The asymptotic and integral closure operations in multiplicative lattice modules

Authors

  • Sylvia M. Foster
  • Johnny A. Johnson

DOI:

https://doi.org/10.5556/j.tkjm.36.2005.107

Abstract

This paper is primarily concerned with the integral and asymptotic closure operations on a multiplicative lattice relative to the greatest element of a lattice module having the ascending chain condition. We show that a cancellation law holds for the asymptotic closure of elements of the multiplicative lattice and we ultimately show, by means of multiplicative filtrations and filtration transforms, that the asymptotic closure of an element in a multiplicative lattice relative to the greatest element of a lattice module, coincides with its integral closure relative to this element in the lattice module.

Author Biographies

Sylvia M. Foster

Department of Mathematics, University of Houston, Houston, Texas 77204-3008, USA.

Johnny A. Johnson

Department of Mathematics, University of Houston, Houston, Texas 77204-3008,USA.

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Published

2005-12-31

How to Cite

Foster, S. M., & Johnson, J. A. (2005). The asymptotic and integral closure operations in multiplicative lattice modules. Tamkang Journal of Mathematics, 36(4), 345-358. https://doi.org/10.5556/j.tkjm.36.2005.107

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Section

Papers