On Artin's Conjecture and Euclid's Algorithm in Global Fields.
In this paper we study commutative rings whose prime ideals are direct sums of cyclic modules. In the case is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring , the following statements are equivalent: (1) Every prime ideal of is a direct sum of cyclic -modules; (2) where is an index set and is a principal ideal ring for each ; (3) Every prime ideal of is a direct sum of at most...
We characterize prime submodules of for a principal ideal domain and investigate the primary decomposition of any submodule into primary submodules of