English

Radical semistar operations

Commutative Algebra 2022-07-18 v1

Abstract

We introduce and study the set of radical stable operations of an integral domain DD. We show that their set is a complete lattice that is the join-completion of the set of spectral semistar operations, and we characterize when every radical operation is spectral (under the hypothesis that DD is rad-colon coherent). When DD is a Pr\"ufer domain such that every set of minimal prime ideals is scattered, we completely classify stable semistar operations.

Keywords

Cite

@article{arxiv.2207.07366,
  title  = {Radical semistar operations},
  author = {Dario Spirito},
  journal= {arXiv preprint arXiv:2207.07366},
  year   = {2022}
}
R2 v1 2026-06-25T00:56:26.622Z