Trivial extensions defined by Prufer conditions

Journal of Pure and Applied Algebra 214 (2010) 53-60 This paper deals with well-known extensions of the Prufer domain concept to arbitrary commutative rings. We investigate the transfer of these notions in trivial ring extensions (also called idealizations) of commutative rings by modules and then g...

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Bibliographic Details
Main Authors Bakkari, C, Kabbaj, S, Mahdou, N
Format Journal Article
LanguageEnglish
Published 02.08.2008
Subjects
Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
Online AccessGet full text
DOI10.48550/arxiv.0808.0275

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Summary:Journal of Pure and Applied Algebra 214 (2010) 53-60 This paper deals with well-known extensions of the Prufer domain concept to arbitrary commutative rings. We investigate the transfer of these notions in trivial ring extensions (also called idealizations) of commutative rings by modules and then generate original families of rings with zerodivisors subject to various Prufer conditions. The new examples give further evidence for the validity of Bazzoni-Glaz conjecture on the weak dimension of Gaussian rings. Moreover, trivial ring extensions allow us to widen the scope of validity of Kaplansky-Tsang conjecture on the content ideal of Gaussian polynomials.
DOI:10.48550/arxiv.0808.0275