St-Polyform modules and related concepts

Abstract EN

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and κ-nonsingular modules.

Various properties of such modules are obtained.

Another characterization of St-polyform module is given.

An existence of St-polyform submodules in certain class of modules is considered.

The relationships of St-polyform with some related concepts are investigated.

Furthermore, we introduce other new classes which are; St-semisimple and κ-non St-singular modules, and we verify that the class of St-polyform modules lies between them