On the hopficity of the polynomial rings

  • S. P. Tripathi


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.


Hopfian rings 


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Copyright information

© Indian Academy of Sciences 1998

Authors and Affiliations

  • S. P. Tripathi
    • 1
  1. 1.Department of Mathematics, K. M. CollegeUniversity of DelhiDelhiIndia

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