TY - JOUR
AU - Foster, Sylvia M.
AU - Johnson, Johnny A.
PY - 2005/12/31
Y2 - 2022/05/26
TI - The asymptotic and integral closure operations in multiplicative lattice modules
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 36
IS - 4
SE -
DO - 10.5556/j.tkjm.36.2005.107
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/107
SP - 345-358
AB - 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.
ER -