On quasi(semi) convex MV-algebras

Abstract In this paper, we equip MV-algebras with convex structures and introduce the notions of semiconvex MV-algebras and quasiconvex MV-algebras by requiring the MV-operations to be semi-convexity-preserving and convexity-preserving, respectively. Moreover, we explore their properties. Based on the previous study of weak convex MV-algebras, we further investigate related issues for weak convex MV-algebras and obtain some new results. Finally, we show that the collection of all lattice ideals on each MV-algebra A forms a convex structure, denoted by C, we further prove that (A, C) is a semiconvex MV-algebra. We also investigate the finite products and quotients of such lattice ideal convex structures on MV-algebras.