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On ideals and congruences of distributive demi-p-algebras

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Abstract

We identify the \({{}^\star}\)-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \({[G,\iota]}\) of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \({{}^\star}\)-ideal, prime \({{}^\star}\)-ideal, and falsity ideal coincide.

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Authors and Affiliations

  1. Mathematical Institute, University of St Andrews, St Andrews, KY16 9SS, Scotland

    T. S. Blyth

  2. School of Computer Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China

    Jie Fang

  3. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, People’s Republic of China

    Leibo Wang

Authors
  1. T. S. Blyth
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  2. Jie Fang
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  3. Leibo Wang
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Corresponding author

Correspondence to T. S. Blyth.

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Presented by Constantine Tsinakis

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Blyth, T.S., Fang, J. & Wang, L. On ideals and congruences of distributive demi-p-algebras. Stud Logica 103, 491–506 (2015). https://doi.org/10.1007/s11225-014-9576-x

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  • DOI: https://doi.org/10.1007/s11225-014-9576-x

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