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On the power-set \(Q\)-algebras

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Abstract

\(Q\)-algebras form an important class of ordered algebraic structures, which can be regarded as a generalization of quantales and \(Q\)-modules, and play an important role in the study of lattice-valued quantales, lattice-valued frames and stratified lattice-valued topological spaces. Every \(Q\)-algebra is isomorphic to a quotient \(Q\)-algebra of some power-set \(Q\)-algebra. We investigate some properties of power-set \(Q\)-algebras, and, by means of the relations between ordered semigroups, give a general characterization for the strong homomorphisms between power-set \(Q\)-algebras.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11171196 and 11301316), the Fundamental Research Funds for the Central Universities (Grant No. GK201402001) and the Research Award for Young Teachers of **’an University of Posts and Telecommunications (ZL2014-38). We would like to thank the anonymous reviewers for their helpful comments and suggestions for the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Shaanxi Normal University, **’an, 710062, People’s Republic of China

    Shengwei Han & Bin Zhao

  2. Department of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, CO, 80208, USA

    Shengwei Han

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  1. Shengwei Han
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  2. Bin Zhao
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Correspondence to Shengwei Han.

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Communicated by Mikhail Volkov.

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Han, S., Zhao, B. On the power-set \(Q\)-algebras. Semigroup Forum 92, 214–227 (2016). https://doi.org/10.1007/s00233-015-9705-5

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