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Minimal prime state filters and state radicals on state pseudo \({ BL}\)-algebras

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Abstract

The aim of this paper is the study of some classes of state filters of a state pseudo BL-algebra. The concepts of minimal prime state filter and of state hyperarchimedean pseudo BL-algebra are introduced and a characterization of a state hyperarchimedean pseudo BL-algebra is presented. Also, we define the notion of a state radical of a state filter of a state pseudo BL-algebra, we present a characterization of a state radical and some of its properties. The algebra of state radicals of a state pseudo BL-algebra is studied.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, Al. I. Cuza Street,13, 200585, Craiova, Romania

    N. M. Constantinescu

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  1. N. M. Constantinescu
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Correspondence to N. M. Constantinescu.

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Communicated by A. Di Nola.

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Constantinescu, N.M. Minimal prime state filters and state radicals on state pseudo \({ BL}\)-algebras. Soft Comput 20, 841–851 (2016). https://doi.org/10.1007/s00500-015-1824-0

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  • DOI: https://doi.org/10.1007/s00500-015-1824-0

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