Trivial extensions defined by Prüfer conditions

DOI10.1016/J.JPAA.2009.04.011zbMATH Open1175.13008arXiv0808.0275OpenAlexW1995403520MaRDI QIDQ1035668

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Publication date: 4 November 2009

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/0808.0275

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