Idempotence and divisorialty in Pr\"ufer-like domains

Marco Fontana; Evan Houston; Mi Hee Park

Idempotence and divisorialty in Pr\"ufer-like domains

Commutative Algebra 2018-11-26 v1 Algebraic Geometry Rings and Algebras

Authors: Marco Fontana , Evan Houston , Mi Hee Park

Abstract

Let $D$ be a Pr\"ufer $\star$ -multiplication domain, where $\star$ is a semistar operation on $D$ . We show that certain ideal-theoretic properties related to idempotence and divisoriality hold in Pr\"ufer domains, and we use the associated semistar Nagata ring of $D$ to show that the natural counterparts of these properties also hold in $D$ .

Keywords

prüfer star-multiplication domain idempotence divisoriality semistar operation nagata ring

Cite

@article{arxiv.1811.09210,
  title  = {Idempotence and divisorialty in Pr\"ufer-like domains},
  author = {Marco Fontana and Evan Houston and Mi Hee Park},
  journal= {arXiv preprint arXiv:1811.09210},
  year   = {2018}
}

Comments

to appear in the Springer Volume, "Rings and Factorizations", Proceedings of the Graz Conference 2018

Idempotence and divisorialty in Pr\"ufer-like domains

Abstract

Keywords

Cite

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