On a New Class of Integral Domains with the Portable Property

David E. Dobbs (), Gabriel Picavet () and Martine Picavet-L’Hermitte ()
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David E. Dobbs: University of Tennessee, Department of Mathematics
Gabriel Picavet: Université Blaise Pascal, UMR6620 CNRS, Les Cézeaux, Laboratoire de Mathématiques
Martine Picavet-L’Hermitte: Université Blaise Pascal, UMR6620 CNRS, Les Cézeaux, Laboratoire de Mathématiques

A chapter in Commutative Algebra, 2014, pp 119-132 from Springer

Abstract: Abstract A (commutative integral) domain R is said to be a pseudo-almost divided domain if for all P ∈ Spec(R) and u ∈ PR P , there exists a positive integer n such that u n ∈ P. Such domains are related to several known kinds of domains, such as divided domains and straight domains. It is shown that “locally pseudo-almost divided” is a portable property of domains. Hence, if T is a domain with a maximal ideal Q and D is a subring of T∕Q, then the pullback R : = T × T ∕ Q D $$R:= T \times _{T/Q}D$$ is locally pseudo-almost divided if and only if both T and D are locally pseudo-almost divided. A similar pullback transfer result is given for the “straight domain” property (which is not known to be portable) by imposing additional restrictions on the data T, Q, D.

Keywords: Integral domain; Pullback; Portable property; Straight domain; Pseudo-almost divided domain; PAVD; APVD; Almost Prüfer domain; Divided domain; Root closed; [2010] Primary; 13G05; Secondary; 13A15; 13F05; 13B21 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0925-4_7

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