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arXiv · 1308.5750

A Note on the Existence of Indecomposable Essential Submodules of the Ring of Quotients of Ore Domains

Juan Orendain
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Abstract

We study the problem of existence of essential indecomposable submodules of direct sums of copies of the ring of quotients of Ore domains. We provide, for each Ore domain $D$, with at least three non-associate irreducibles, a lower bound for the supremum of all cardinals $κ$ such that the direct sum of $κ$ copies of the ring of quotients of $D$ contains indecomposable essential $D$-submodules, and a lower bound for the number of times this bound is attained up to isomorphisms. We provide examples illustrating these results.

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BibTeXRIS

Juan Orendain. 2014-03-26. A Note on the Existence of Indecomposable Essential Submodules of the Ring of Quotients of Ore Domains. https://arxiv.org/abs/1308.5750

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