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Relativizations of relation algebras by the diversity

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Abstract

The elements of a relation algebra A that are below a fixed elementa form a relative subalgebrab Aa of A. It was shown by H. Andréka that the class of all relative subalgebras of relation algebras is not a variety, but it follows immediately from results of R. L. Kramer that the closure of this class under subalgebras is a finitely based variety. We show that the relative subalgebras A0′ with 0′ the diversity element of A, form a finitely based variety. We also show that A is determined by A0′, up to a direct factor that is Boolean (the relative product coincides with the meet).

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    J. Rafter

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  1. J. Rafter
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Rafter, J. Relativizations of relation algebras by the diversity. Algebra Universalis 35, 342–358 (1996). https://doi.org/10.1007/BF01197179

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  • DOI: https://doi.org/10.1007/BF01197179

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