Generalized Cardinal Properties of Lattices and Lattice Ordered Groups

摘要

We denote by K the class of all cardinals; put K' = K ∪ {∞}. Let L be a class of algebraic systems. A generalized cardinal property f on L is defined to be a rule which assings to each A ∈ L an element fA of K' such that, whenever A_1, A_2 ∈ L and A_1 approx= A_2, then fA_1 = fA_2. In this paper we are interested mainly in the cases when (i) L is the class of all bounded lattices B having more than one element, or (ii) L is a class of lattice ordered groups.