Abstract

We introduce the variety $\scr{L}_{n}^{m}$ , m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety $\scr{L}_{n}^{m}$ is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety $\scr{L}_{n}^{m}$ contains the variety of Łukasiewicz algebras of order n