M-zeroids: structure and categorical equivalence (Q1928484)

Since \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467--490 (1958; Zbl 0084.00704)] first defined the algebraic systems called MV-algebras, numerous generalizations for MV-algebras have been proposed, including the structures called m-zeroids. In this paper the authors develop a method for constructing finite totally-ordered m-zeroids. They also prove that there is a categorical equivalence between the category of pseudo Łukasiewicz-like implicators and the category of finite totally-ordered m-zeroids.