Monoidal semifilters and arrays of prime ideals

Abhishek Banerjee¹

¹ Department of Mathematics Indian Institute of Science Bangalore 560012, India

Fundamenta Mathematicae, Tome 237 (2017) no. 3, pp. 281-296

Résumé

Let $R$ be a commutative ring. If $A\subseteq R$ is an ideal and $\mathcal F$ is a monoidal semifilter of ideals in $R$, we say that a prime ideal $P$ is a realization of $(A,\mathcal F)$ if $P\supseteq A$ and $P\notin \mathcal F$. We give “if and only if” conditions for the existence of a realization of a family $\{(A_t,\mathcal F_t)\}_{t\in T}$ of such pairs indexed by a finite rooted tree $T$. We also apply our results to trees of prime ideals outside a given monoidal semifilter in a tensor product of algebras.

Détail

DOI : 10.4064/fm218-8-2016

Keywords: commutative ring subseteq ideal mathcal monoidal semifilter ideals say prime ideal realization mathcal supseteq notin mathcal only conditions existence realization family mathcal pairs indexed finite rooted tree apply results trees prime ideals outside given monoidal semifilter tensor product algebras