SOME ASPECTS OF MODULAR LATTICES WITH DUAL KRULL DIMENSION.

For an ordinal α, a modular lattice L with 0 and 1 is α-atomic if L has dual Krull dimension α but each interval [0,x] with x < 1 has dual Krull dimension <α. The properties of α-atomic lattices are presented and applied to module theory. The endomorphism ring of certain types of α-atomic modules is a local domain and hence there is a Krull–Schmidt type theorem for those α-atomic modules. [ABSTRACT FROM AUTHOR]