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Complexity of Elements in Rings

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Abstract

If R is a ring with subset S then the rational closure Div R (S) of S in R is the smallest subring D of R containing S such that U(D)=D∩U(R) where U(D), resp. U(R), denotes the group of units of D resp. R. In this paper a new approach to the so-called complexity is given in order to describe how the elements of Div R (S) are built from elements of S.

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Authors and Affiliations

  1. Department of Mathematics, Vladimir State University, Gorki Street 87, 600026, Vladimir, Russia

    N. I. Dubrovin

  2. Institut für Mathematik, Universität Potsdam, Postfach 601553, 14469, Potsdam, Germany

    J. Gräter & T. Hanke

Authors
  1. N. I. Dubrovin
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  2. J. Gräter
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  3. T. Hanke
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Dubrovin, N.I., Gräter, J. & Hanke, T. Complexity of Elements in Rings. Algebras and Representation Theory 6, 33–45 (2003). https://doi.org/10.1023/A:1022320103094

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  • DOI: https://doi.org/10.1023/A:1022320103094

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