Modules whose small submodules have Krull dimension

Modules Whose Small Submodules Have Krull Dimension

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

δ-Small Submodules and δ-Supplemented Modules

Upper bounds for noetherian dimension of all injective modules with Krull dimension

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

Research Article -Small Submodules and -Supplemented Modules

Krull Dimension

1 Introduction