ar X iv : 0 80 8 . 02 75 v 1 [ m at h . A C ] 2 A ug 2 00 8 TRIVIAL EXTENSIONS DEFINED BY PRÜFER CONDITIONS

Abstract

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 zerodivisors subject to various Prüfer 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.

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Cite this paper

@inproceedings{BAKKARI2009arXI, title={ar X iv : 0 80 8 . 02 75 v 1 [ m at h . A C ] 2 A ug 2 00 8 TRIVIAL EXTENSIONS DEFINED BY PR{\"{U}FER CONDITIONS}, author={C . BAKKARI and Samir Kabbaj and Najib Mahdou}, year={2009} }