Abstract
The central result of this paper provides a simple equational basis for the join, IRL∨LG, of the variety LG of lattice-ordered groups (ℓ-groups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRL∨LG=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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Jónsson, B., Tsinakis, C. Products of Classes of Residuated Structures. Studia Logica 77, 267–292 (2004). https://doi.org/10.1023/B:STUD.0000037130.29400.97
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DOI: https://doi.org/10.1023/B:STUD.0000037130.29400.97