Research Article -Small Submodules and -Supplemented Modules

Oplus-supplemented modules with respect to images of a fully invariant submodule

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

δ-Small Submodules and δ-Supplemented Modules

Generalized Supplemented Modules

Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GASmodule and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P ∗); (3)...

A generalization of $oplus$-cofinitely supplemented modules

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

A note on primary-like submodules of multiplication modules

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...