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On Hopfian Rings

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Abstract

The main results proved in this paper are:

(i) If R is a boolean hopfian ring then the polynomial ring R[T] is hopfian.

(ii) Let R and S be hopfian rings. Suppose the only central idempotents in S are 0 and 1 and that S is not a homomorphic image of R. Then R × S is a hopfian ring.

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References

  1. M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison Wesley Publishing Company (1969).

  2. S. Deo and K. Varadarajan, Hopfian and co-hopfian zero-dimensional spaces, J. Ramanujan Math. Soc., 9 (1994), 177–202.

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  3. G. F. Simmons, Introduction to Toplogy and Modern Analysis, McGraw-Hill Book Company (1963).

  4. K. Varadarajan, Hopfian and co-hopfian objects, Publicationes Math., 36 (1992), 293–317.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

    K. Varadarajan

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  1. K. Varadarajan
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Varadarajan, K. On Hopfian Rings. Acta Mathematica Hungarica 83, 17–26 (1999). https://doi.org/10.1023/A:1006655217670

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  • DOI: https://doi.org/10.1023/A:1006655217670

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