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Variations and Tensor Products of M-Acts

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Abstract

For a variety K of algebras, it is well known that the Hom-functor is in general not functional; that is, Hom(A,B) is in general not a subalgebra of the |A|-fold product B|A| of B. In this paper we take K to be the category of M-acts, for a monoid M, and investigate the above problem for a class of more general set-valued functors Hα, usually called the functor of semihomomorphisms. Characterizing functionality for these functors, we define bimorphisms (bivariations) with respect to these functors and investigate the interdependence between the universal bivariations, tensor product, and functionality.

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Authors and Affiliations

  1. Department of Mathematics and Center of Excellence in Algebraic and Logical Structures in Discrete Mathematics, Shahid Beheshti University, Tehran, Iran

    M.M. Ebrahimi

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  1. M.M. Ebrahimi
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Correspondence to M.M. Ebrahimi.

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Ebrahimi, M. Variations and Tensor Products of M-Acts. Semigroup Forum 75, 446–456 (2007). https://doi.org/10.1007/s00233-007-0729-3

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  • DOI: https://doi.org/10.1007/s00233-007-0729-3

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