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arXiv · 1006.0159

Amalgamation of rings defined by bézout-like conditions

Mohammed Kabbour·Najib Mahdou
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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 $E^2\subseteq E.$

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Mohammed Kabbour, Najib Mahdou. 2010-06-01. Amalgamation of rings defined by bézout-like conditions. https://arxiv.org/abs/1006.0159

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