Using Vaggione’s concept of central element in a double pointed algebra, we introduce the notion of Boolean like variety as a generalization of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double pointed variety is discriminator i↵ it is semi-Boolean like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterization of double pointed discriminator varieties. Moreover, we show that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional regular operations.

Boolean like algebras

SALIBRA, Antonino
2013-01-01

Abstract

Using Vaggione’s concept of central element in a double pointed algebra, we introduce the notion of Boolean like variety as a generalization of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double pointed variety is discriminator i↵ it is semi-Boolean like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterization of double pointed discriminator varieties. Moreover, we show that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional regular operations.
2013
Proceedings of the 6th Topology, Algebra and Categories in Logic (TACL 2013)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3260460
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