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Monadic classes of quantum B-algebras

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Abstract

The aim of this paper is to define the monadic quantum B-algebras and to investigate their properties. If the monadic operators are isotone, we show that they form a residuated pair. Special properties are studied for the particular case of monadic quantum B-algebras with pseudo-product, and a representation theorem for monadic quantum B-algebras with pseudo-product is proved. The monadic filters of monadic quantum B-algebras are defined, and their properties are studied. We prove that there is an isomorphism between the lattice of all filters of a monadic quantum B-algebra and the lattice of all filters of its subalgebra of fixed elements. Monadic operators on unital quantales are introduced, and the functional monadic quantale is constructed.

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Acknowledgements

The author is very grateful to the anonymous referees for their useful remarks and suggestions on the subject that helped improving the presentation.

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  1. Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA, 52242-1419, USA

    Lavinia Corina Ciungu

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  1. Lavinia Corina Ciungu
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Correspondence to Lavinia Corina Ciungu.

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Ciungu, L.C. Monadic classes of quantum B-algebras. Soft Comput 25, 1–14 (2021). https://doi.org/10.1007/s00500-020-05404-7

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