Monadic GMV-algebras
In a recent paper, there appeared plenty new algebraic models that were inspired by Łukasiewicz many-valued calculus. They generalized MV-algebras not assuming commutativity any more. One such algebraic model are the GMV-algebras, introduced by the first author and independently by \textit{G. Georgescu} and \textit{A. Iorgulescu} [``Pseudo-MV algebras'', Mult.-Valued Log. 6, No. 1--2, 95--135 (2001; Zbl 1014.06008)]. These algebras are always an interval in a unital \(\ell\)-group with strong unit. The authors introduce monadic GMV-algebras and study also polyadic GMV-algebra. Some relations among ideals and congruences, and among varieties are shown.
scientific article; zbMATH DE number 5313051