Published in Volume XXXIII, Issue 1, 2023, pages 79-92, doi: 10.7561/SACS.2023.1.79

Authors: H. Machida


A centralizing monoid M is a set of unary operations which commute with some set F of operations. Here, F is called a witness of M . On a 3-element set, a centralizing monoid is maximal if and only if it has a constant operation or a majority minimal operation as its witness.

In this paper, we take one such majority operation, which corresponds to a maximal centralizing monoid, on a 3-element set and obtain its generalization, called mb , on a k-element set for any k ≥ 3. We explicitly describe the centralizing monoid M(mb ) with mb as its witness and then prove that it is not maximal if k > 3, contrary to the case for k = 3.

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  title={A Study on Centralizing Monoids with Majority Operation Witnesses},
  author={Hajime Machida},
  journal={Scientific Annals of Computer Science},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},