Polynomial rings over commutative reduced Hopfian local rings |
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Authors: | A M Dhorajia H Mukherjee |
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Institution: | 1.Birla Institute of Technology and Science,Pilani,India |
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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 Rx] 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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