Small duo and Fully small stable modules

Abstract

New types of modules, namely fully small stable and small duo modules over a ring are introduced and investigated. These concepts lead to study the relation between these types and other classes of modules; such as, uniserial, some classes of multiplication and quasi-injective modules. It is shown that a projective module is small duo if and only if it is a small multiplication. Also, uniserial Artinian module is fully small stable. In addition, if R is a commutative ring then a fully small stable module is equivalent to small duo and small principally quasi injective. Also, we discuss full small stability of direct sum of modules.