Products of classes of residuated structures

Studia Logica 77 (2):267 - 292 (2004)
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Abstract

The central result of this paper provides a simple equational basis for the join, IRLLG, of the variety LG of lattice-ordered groups (-groups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRLLG=IRL×LG. In the process of deriving our result, we will obtain simple axiomatic bases for other products of classes of residuated structures, including the class IRL×s LG, consisting of all semi-direct products of members of IRL by members of LG. We conclude the paper by presenting a general method for constructing such semi-direct products, including wreath products.

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Citations of this work

Non-Commutative Logical Algebras and Algebraic Quantales.Wolfgang Rump & Yi Chuan Yang - 2014 - Annals of Pure and Applied Logic 165 (2):759-785.
Quasi-Subtractive Varieties.Tomasz Kowalski, Francesco Paoli & Matthew Spinks - 2011 - Journal of Symbolic Logic 76 (4):1261-1286.
On Birkhoff’s Common Abstraction Problem.F. Paoli & C. Tsinakis - 2012 - Studia Logica 100 (6):1079-1105.

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