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Generalized affine transformation monoid of a free module of finite rank over finite chain rings

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Abstract

Let R be a finite commutative chain ring, n a positive integer and R n the free R-module of rank n consisting of column vectors over R. The generalized affine transformation monoid Gaff n (R) of R n is introduced, then Schützenberger groups of -classes, principal factors and group -classes of the monoid Gaff n (R) are investigated. As corollaries, basic numerical information of Gaff n (R) is given.

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Authors and Affiliations

  1. School of Sciences, Shandong University of Technology, Zibo, Shandong, 255091, P.R. China

    Yonglin Cao

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  1. Yonglin Cao
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Correspondence to Yonglin Cao.

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Communicated by Thomas E. Hall.

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Cao, Y. Generalized affine transformation monoid of a free module of finite rank over finite chain rings. Semigroup Forum 83, 190–204 (2011). https://doi.org/10.1007/s00233-011-9296-8

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  • DOI: https://doi.org/10.1007/s00233-011-9296-8

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