lattice with section antitone involution; basic algebra; commutative basic algebra; MV-algebra
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
 Botur, M., Halaš, R.: Finite commutative basic algebras are MV-algebras. (to appear) in Multiple-Valued Logic and Soft Computing.
 Chajda, I.: Lattices and semilattices having an antitone involution in every upper interval
. Comment. Math. Univ. Carol. 44 (2003), 577-585. MR 2062874
| Zbl 1101.06003
 Chajda, I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions
. Acta Sci. Math. (Szeged) 71 (2005), 19-33. MR 2160352
| Zbl 1099.06006
 Cignoli, R. L. O., D'Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning
. Kluwer Acad. Publ., Dordrecht (2000). MR 1786097
| Zbl 0937.06009