Algebra universalis

, Volume 73, Issue 3–4, pp 369–390 | Cite as

The connection of skew Boolean algebras and discriminator varieties to Church algebras

Article

Abstract

We establish a connection between skew Boolean algebras and Church algebras. We prove that the set of all semicentral elements in a right Church algebra forms a right-handed skew Boolean algebra for the properly defined operations. The main result of this paper states that the variety of all semicentral right Church algebras of type \({\tau}\) is term equivalent to the variety of right-handed skew Boolean algebras with additional regular operations. As a corollary to this result, we show that a pointed variety is a discriminator variety if and only if it is a 0-regular variety of right-handed skew Boolean algebras.

2010 Mathematics Subject Classification

Primary: 03G10 Secondary: 08B26 

Keywords and phrases

skew Boolean algebra Church algebra discriminator variety factor congruence decomposition operator 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Department of Environmental Sciences, Informatics andStatisticsUniversità Ca’Foscari VeneziaVeneziaItaly

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