Algebraic Geometry Over Complete Lattices and Involutive Pocrims

Abstract

Abstract An involutive pocrim is a resituated integral partially ordered commutative monoid with an involution operator, consider as an algebra. In this paper it is proved that the variety of a finitely generated by involutive pocrims of finite type has a finitely based equational theory. We also study the algebraic geometry over compete lattices and we investigate the properties of being equationally Noetherian and uω-compact over such lattices.