Abstract. In this paper we establish some equivalent conditions for a $C$-lattice to be an almost discrete valuation lattice. We characterize weak invertible lattices (or {\it WI}-lattices) in terms of Baer lattices and quasiregular lattices. We give some equivalent conditions for a $C$-lattice to be a Dedekind lattice.

AMS Subject Classification (1991): 06F10, 06F05, 06F99, 13A15

Keyword(s): multiplicative lattice, Noether latttice, principal element, Dedekind, invertible

Received February 20, 1997 and in revised form April 28, 1997. (Registered under 5771/2009.)