Cyclic elements and subalgebras of GMV-algebras (Q2380336)

In this paper, some properties of GMV-algebras (i.e., the non-commutative generalization of MV-algebras) are studied in relationship with the existence of cyclic elements. A GMV-algebra has a cyclic element of order \(n\) if it contains a copy of the MV-algebra \(\Gamma(Z,n)=\{0,1/n, \dots, 1\}\). Extending a result in [\textit{A. Torrens}, ``Cyclic elements in MV-algebras and Post algebras'', Math. Log. Q. 40, No.~4, 431--444 (1994; Zbl 0815.06009)], the author describes some classes of GMV-algebras that contain the greatest subalgebra belonging to the variety generated by \(\Gamma(Z,n)\). Further, cyclic elements are used to describe some special case of free products of GMV-algebras.