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\(\delta \)-ideals of a pseudocomplemented semilattice

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Abstract

In this paper we study \(\delta \)-ideals of a pseudocomplemented semilattice. We give some characterizations of \(\delta \)-ideals. We also prove Stone type separation theorem for \(\delta \)-ideals of a pseudocomplemented semilattice. We show that the set of \(\delta \)-ideals of a pseudocomplemented semilattice form a distributive pseudocomplemented lattice. We also prove that the set of principal \(\delta \)-ideals form a Boolean algebra.

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Authors and Affiliations

  1. Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, 3114, Bangladesh

    M. R. Talukder, H. S. Chakraborty & S. N. Begum

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  1. M. R. Talukder
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  2. H. S. Chakraborty
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  3. S. N. Begum
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Correspondence to M. R. Talukder.

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Talukder, M.R., Chakraborty, H.S. & Begum, S.N. \(\delta \)-ideals of a pseudocomplemented semilattice. Afr. Mat. 32, 419–429 (2021). https://doi.org/10.1007/s13370-020-00834-w

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  • DOI: https://doi.org/10.1007/s13370-020-00834-w

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