Generalized Cardinal Properties of Lattices and Lattice Ordered Groups

We denote by K the class of all cardinals; put K = K {}. Let be a class of algebraic systems. A generalized cardinal property f on is defined to be a rule which assings to each A an element fA of K such that, whenever A₁, A₂ and A₁ A₂, then fA₁ = fA₂. In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices B having more than one element, or (ii) is a class of lattice ordered groups.