Local dimension is an ordinal valued invariant that is in some sense a measure of how far a
ring is from being local and denoted ldim (R). The purpose of this paper is to study the local …

We say that a class 𝒫 of right modules over a fixed ring R is an epic class if it is closed under
homomorphic images. For an arbitrary epic class 𝒫, we define a 𝒫-dimension of modules …

We say that a class Q of left R-modules is a monic class if a nonzero submodule of a module
in Q is also a module in Q. For a monic class Q, we define a Q-dimension of modules that …

A generalization of Köthe rings is the family of rings whose ideals are direct sums of cyclic
modules. These rings were previously studied in the commutative local case. This motivated …

In this paper we study rings with local dimension which certain of ideals are direct sum of
cyclic modules. It is shown that for a commutative ring R with local dimension ω, every ideal …