Mathematics – Commutative Algebra
Scientific paper
2008-08-02
Mathematics
Commutative Algebra
12 pages. Theorem 2.1(3) is improved via modification of Lemma 2.3
Scientific paper
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.
Bakkari Chahrazade
Kabbaj Salah
Mahdou Najib
No associations
LandOfFree
Trivial extensions defined by Prufer conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trivial extensions defined by Prufer conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trivial extensions defined by Prufer conditions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-662410