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Polynomial rings over commutative reduced Hopfian local rings

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Abstract

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 [16], 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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  1. Birla Institute of Technology and Science, Pilani, India

    A. M. Dhorajia & H. Mukherjee

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  1. A. M. Dhorajia
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  2. H. Mukherjee
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Correspondence to A. M. Dhorajia.

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Dhorajia, A.M., Mukherjee, H. Polynomial rings over commutative reduced Hopfian local rings. Acta Math. Hungar. 154, 243–251 (2018). https://doi.org/10.1007/s10474-017-0782-7

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  • DOI: https://doi.org/10.1007/s10474-017-0782-7

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