First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime -modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.
Let be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication -module (see [8], [12] and [3]).
Let be a lattice with the greatest element . Following the concept of generalized small subfilter, we define -supplemented filters and investigate the basic properties and possible structures of these filters.
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
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