Structure on the set of closure operations of a commutative ring

Janet C. Vassilev

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arXiv · 0809.2021

Structure on the set of closure operations of a commutative ring

Janet C. Vassilev

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

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Janet C. Vassilev. 2008-09-11. Structure on the set of closure operations of a commutative ring. https://arxiv.org/abs/0809.2021

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