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arXiv · 1308.0727

Lattice of Ideals of the Polynomial Ring over a Commutative Chain Ring

Xiang-dong Hou
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Abstract

Let $R$ be a commutative chain ring. We use a variation of Gröbner bases to study the lattice of ideals of $R[x]$. Let $I$ be a proper ideal of $R[x]$. We are interested in the following two questions: When is $R[x]/I$ Frobenius? When is $R[x]/I$ Frobenius and local? We develop algorithms for answering both questions. When the nilpotency of $\text{rad}\,R$ is small, the algorithms provide explicit answers to the questions.

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Xiang-dong Hou. 2013-08-03. Lattice of Ideals of the Polynomial Ring over a Commutative Chain Ring. https://arxiv.org/abs/1308.0727

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