Products of classes of residuated structures

Studia Logica 77 (2):267 - 292 (2004)
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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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Non-Commutative Logical Algebras and Algebraic Quantales.Wolfgang Rump & Yi Chuan Yang - 2014 - Annals of Pure and Applied Logic 165 (2):759-785.
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