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Embedding Theorems and Maximal Subsemigroups of Some Linear Transformation Semigroups with Restricted Range

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Ukrainian Mathematical Journal Aims and scope

Let V be a vector space over a field and let T(V) denote the semigroup of all linear transformations from V into V. For a fixed subspace W of V, let F(V,W) be the subsemigroup of T(V ) formed by all linear transformations α from V into W such that V α ⊆ W α. We prove that any regular semigroup S can be embedded in F(V,W) with dim(V) = |S1| and dim(W) = |S|, and determine all maximal subsemigroups of F(V,W) in the case where W is a finite-dimensional subspace of V over a finite field.

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Authors and Affiliations

  1. Chiang Mai Rajabhat University, Chiang Mai, Thailand

    W. Sommanee

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  1. W. Sommanee
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Correspondence to W. Sommanee.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 12, pp. 1714–1722, December, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i12.1289.

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Sommanee, W. Embedding Theorems and Maximal Subsemigroups of Some Linear Transformation Semigroups with Restricted Range. Ukr Math J 73, 1985–1996 (2022). https://doi.org/10.1007/s11253-022-02042-0

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  • DOI: https://doi.org/10.1007/s11253-022-02042-0

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