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Minimal varieties of involutive residuated lattices. (English) Zbl 1101.06010

Summary: We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice.

MSC:

06F05 Ordered semigroups and monoids
06B20 Varieties of lattices
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