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Cyclic elements and subalgebras of GMV-algebras

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Abstract

We study cyclic elements of order n of GMV-algebras. The existence of cyclic elements is equivalent to the condition that a given GMV-algebra contains a copy of the MV-algebra \(\Upgamma({\mathbb Z},n).\) Using cyclic elements, we describe necessary conditions which guarantee the existence of a greatest subalgebra belonging to the variety generated by \(\Upgamma({\mathbb Z},n).\) This is true, e.g. for representable GMV-algebras. Finally, we use cyclic elements to prove the existence of a free product in various varieties of GMV-algebras.

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Acknowledgments

The author is indebted to the referee for his very careful reading and suggestions. The paper has been supported by the Center of Excellence SAS—Physics of Information—I/2/2005, the grant VEGA No. 2/6088/26 SAV, by Science and Technology Assistance Agency under the contract APVV-0071-06, Bratislava, Slovakia.

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  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Dvurečenskij, A. Cyclic elements and subalgebras of GMV-algebras. Soft Comput 14, 257–264 (2010). https://doi.org/10.1007/s00500-009-0400-x

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