Trivial extensions defined by Prüfer conditions

This paper deals with well-known extensions of the Prüfer 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 zero-divisors...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 214; no. 1; pp. 53 - 60
Main Authors Bakkari, C., Kabbaj, S., Mahdou, N.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2010
Subjects
13A15
13B25
13F05
13D05
13B05
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ISSN0022-4049
1873-1376
DOI10.1016/j.jpaa.2009.04.011

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Summary:This paper deals with well-known extensions of the Prüfer 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 zero-divisors subject to various Prüfer conditions. The new examples give further evidence for the validity of the Bazzoni–Glaz conjecture on the weak global 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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2009.04.011