Structure on the set of closure operations of a commutative ring

Details Structure on the set of closure operations of a commutative ring Structure on the set of closure operations of a commutative ring

2008-09-11

arxiv.org/abs/0809.2021v1

Mathematics

Commutative Algebra

Scientific paper

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 $K[[t^2, t^3]]$.

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