Structure on the set of closure operations of a commutative ring
Commutative Algebra
2008-09-12 v1
Abstract
We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid; however, it is the union of two monoids, one being the left but not right act of the other. We also determine all semiprime operations over the ring .
Keywords
Cite
@article{arxiv.0809.2021,
title = {Structure on the set of closure operations of a commutative ring},
author = {Janet C. Vassilev},
journal= {arXiv preprint arXiv:0809.2021},
year = {2008}
}