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nvolutorial Płonka sums

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Abstract

The construction of the sum of a direct (semilattice ordered) system of algebras introduced by J. Plonka – later known as ‘the Plonka sum’ – is one of the most important methods of composition in universal algebra, having a number of applications in different algebraic theories, such as semigroup theory, semiring theory, etc. In this paper we present a more general way for constructing algebras with involution, that is, algebraic systems equipped with a unary involutorial operation which is at the same time an antiautomorphism of the underlying algebra. It is the sum – involutorial Plonka sum, as we call it – of an involution semilattice ordered system of algebras. We investigate its basic properties, as well as the problem of its subdirect decomposition.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovica 4, 21000, Novi, Sad Serbia

    Igor Dolinka

  2. Department of Mathematics, Faculty of Mechanical Engineering, University of Banja Luka, Danka Mitrova 10, 78000, Banja Luka, Bosnia and Herzegovina

    Milovan Vinčić

Authors
  1. Igor Dolinka
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  2. Milovan Vinčić
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Dolinka, I., Vinčić, M. nvolutorial Płonka sums. Periodica Mathematica Hungarica 46, 17–31 (2003). https://doi.org/10.1023/A:1025797422998

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  • DOI: https://doi.org/10.1023/A:1025797422998

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