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arXiv · 1704.06102

Polynomial Rings Over Commutative Reduced Hopfian Local Rings

Alpesh M. Dhorajia·Himadri Mukherjee
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Abstract

In this paper we prove that if $R$ is a commutative, reduced, local ring, then $R$ is Hopfian if and only if the ring $R[x]$ is Hopfian. This answers a question of Varadarajan, in the case when $R$ is a reduced local ring. We provide examples of non-Noetherian Hopfian commutative domains by proving that the finite dimensional domains are Hopfian. Also, we derive some general results related to Hopfian rings.

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Alpesh M. Dhorajia, Himadri Mukherjee. 2017-04-20. Polynomial Rings Over Commutative Reduced Hopfian Local Rings. https://arxiv.org/abs/1704.06102

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