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Growth and uniqueness of rank

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Abstract

We prove that algebras of sub-exponential growth and, more generally, rings with a sub-exponential “growth structure” have the unique rank property. In the opposite direction the proof shows that if the rank is not unique one gets lower bounds on the exponent of growth. Fixing the growth exponent it shows that an isomorphism between free modules of greatly differing ranks can only be implemented by matrices with entries of logarithmically proportional high degrees.

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Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Eli Aljadeff & Shmuel Rosset

Authors
  1. Eli Aljadeff
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  2. Shmuel Rosset
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Aljadeff, E., Rosset, S. Growth and uniqueness of rank. Israel J. Math. 64, 251–256 (1988). https://doi.org/10.1007/BF02787226

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  • DOI: https://doi.org/10.1007/BF02787226

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