Amalgamation of rings defined by bézout-like conditions

2010/06/01 by Kabbour, Mohammed, Mahdou, Najib
#13D02 #13D05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.0159

Abstract

Let f:A\lo B be a ring homomorphism and let J be an ideal of B. In this paper, we investigate the transfer of notions elementary divisor ring, Hermite ring and Bézout ring to the amalgamation A\bowtie^fJ. We provide necessary and sufficient conditions for A\bowtie^fJ to be an elementary divisor ring where A and B are integral domains. In this case it is shown that A\bowtie^fJ is an Hermite ring if and only it is a Bézout ring. In particular, we study the transfer of the previous notions to the amalgamated duplication of a ring A along an A-submodule E of Q(A) such that E²⊆ E.

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