Titlebook: Advances in Commutative Algebra; Dedicated to David F Ayman Badawi,Jim Coykendall Book 2019 Springer Nature Singapore Pte Ltd. 2019 Commuta

Formidable

Optimierung nach dem BPR-Projekt Therefore, the .-local domains (i.e., the local domains, with maximal ideal being a .-ideal) are “cousins” of valuation domains, but, as we will see in detail, not so close. Indeed, for instance, a localization of a .-local domain is not necessarily .-local, but of course a localization of a valuat

Aggregate

https://doi.org/10.1007/978-3-663-14687-2 (., .) is said to be a strongly divided pair if, for each ring . such that . and each . such that ., one has .. Let . be the integral closure of . in .. Then (., .) is a strongly divided pair if and only if . and . have the same sets of nonmaximal prime ideals and, for each maximal ideal . of ., .

Accomplish

PLIC

https://doi.org/10.1007/978-3-642-01588-5 any commutative ring ., the polynomial ring . is additively regular, moreover if ., then . is regular when . is regular. We introduce several stronger types of additively regular rings where the choice for . is restricted: . is strongly additively regular if for each pair of elements . with . regul

叙述

https://doi.org/10.1007/1-4020-2198-4ere is an equation . with . for .. The set of all elements that are .-integral over . is called the .-integral closure of .. This paper surveys recent literature which studies .-reductions and .-integral closure of ideals in arbitrary domains as well as in special contexts such as Prüfer .-multiplic

ULCER

RENAL

heterodox

ATRIA

https://doi.org/10.1007/1-4020-2198-4ces . and . are adjacent if and only if .. The . of . with respect to the ideal ., denoted by ., is the graph on vertices . for some ., where distinct vertices . and . are adjacent if and only if .. In this paper, we cover two main topics: isomorphisms and planarity of zero-divisor graphs. For each

Debark

https://doi.org/10.1007/978-981-13-7028-1Commutative Ring; Zero-divisor Graph; Integral Domains; Pseudographs; Classical Rings; combinatorics