Wajsberg algebras and Post algebras
type: Item
instance of: scholarly article
title: Wajsberg algebras and Post algebras
zbMATH Open document ID: 0808.03048
DOI: 10.1007/BF01053019
author: A. Rodríguez
author: Antoni Torrens
published in: Studia Logica
publication date: 1995-03-15T00:00:00Z
review text: An algebra \(A= \langle A,\to,\neg\rangle\) is said to be a Wajsberg algebra if it satisfies the following equations: \[ \begin{aligned} (a\to b)\to b&= b \\ (a\to b)\to((b\to c)\to (a\to c))&= a\to a \\ (a\to b)\to b&= (b\to a)\to a \\ (\neg a\to \neg b)\to (b\to a)&= a\to a \end{aligned} \] Any finite subdirectly irreducible Wajsberg algebra is quasiprimal and semiprimal, but not each of them is primal. The author gives equational conditions under which the appropriate variety of Wajsberg algebras with additional constants is generated by a primal algebra. The same algebras (and only these algebras) without additional constants admit a lattice reduct which is a P-algebra (P-algebras are a generalization of Post algebras introduced by G. Epstein and A. Horn).
Mathematics Subject Classification ID: 03G20
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D25
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 536888
zbMATH Keywords: Post algebra
zbMATH Keywords: subdirectly irreducible algebra
zbMATH Keywords: chain
zbMATH Keywords: Wajsberg algebra
zbMATH Keywords: variety
zbMATH Keywords: primal algebra
zbMATH Keywords: P-algebra
reviewed by: V. Yu. Meskhi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 536888