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Effect-like algebras induced by means of basic algebras

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Mathematica Slovaca

Abstract

Having an MV-algebra, we can restrict its binary operation addition only to the pairs of orthogonal elements. The resulting structure is known as an effect algebra, precisely distributive lattice effect algebra. Basic algebras were introduced as a generalization of MV-algebras. Hence, there is a natural question what an effect-like algebra can be reached by the above mentioned construction if an MV-algebra is replaced by a basic algebra. This is answered in the paper and properties of these effect-like algebras are studied.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, CZ-779 00, Olomouc, Czech Republic

    Ivan Chajda

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  1. Ivan Chajda
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Correspondence to Ivan Chajda.

Additional information

Communicated by Anatolij Dvurečcenskij

Supported by the Research and Development Council of the Czech Government via the project MSM 6198959214.

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Chajda, I. Effect-like algebras induced by means of basic algebras. Math. Slovaca 60, 21–32 (2010). https://doi.org/10.2478/s12175-009-0164-x

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  • DOI: https://doi.org/10.2478/s12175-009-0164-x

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