Abstract
In this paper we prove that if a ringR satisfies the condition that for some integern > 1,a n =a for everya inR, thenR a hopfian ring implies that the ringR [T] of polynomials is also hopfian. This generalizes a recent result of Varadarajan which states that ifR is a Boolean hopfian ring then the ringR[T] is also hopfian. We show furthermore that there are numerous ringsR satisfying the hypothesis of our theorem which are neither Boolean nor Noetherian.
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Tripathi, S.P. On the hopficity of the polynomial rings. Proc. Indian Acad. Sci. (Math. Sci.) 108, 133–136 (1998). https://doi.org/10.1007/BF02841546
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DOI: https://doi.org/10.1007/BF02841546