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Reductive Modes

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Abstract

A mode is an idempotent and entropic algebra. We show that each variety Rm of m-step left reductive Ω-modes is the Mal'cev product (relative to modes) of Rkand Rm-k. The dual result holds for varieties R 1n of n-step right reductive Ω-modes. The main result says that the join Rm V R 1n is independent and coincides with the Mal'cev product Rm ∘ R 1n . We also give an equational characterization of this variety, and discuss the structure of such modes.

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Authors and Affiliations

  1. Institute of Mathematics Warsaw Technical University, Pl. Politechniki 1, 00-661, Warsaw, Poland E-mail

    A. Pilitowska & A. Romanowska

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  1. A. Pilitowska
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  2. A. Romanowska
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Pilitowska, A., Romanowska, A. Reductive Modes. Periodica Mathematica Hungarica 36, 67–78 (1998). https://doi.org/10.1023/A:1004612003441

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