One of the generalizations supplemented modules is Goldie*-supplemented module, defined by Birkenmeier et al. using $\beta^{\ast}$ relation. In this work, we deal with concept cofinitely as a version module. A left $R$-module $M$ called module if there supplement submodule $S$ $C\beta^{\ast}S$, for each cofinite $C$ $M$. Evidently, are Goldie*-supplemented. Further, Goldie*-supplemented, then $...

In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly module. Then every finitely M-generated module is supplemented. R any ring. if only generated R-module an e-supplement submodule in

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module

We introduce the concepts of lifting modules and (quasi-)discrete modules relative to a given left module. We also introduce the notion of SSRS-modules. It is shown that (1) if M is an amply supplementedmodule and 0→N ′ →N →N ′′ → 0 an exact sequence, then M isN-lifting if and only if it isN ′-lifting andN ′′-lifting; (2) ifM is a Noetherianmodule, then M is lifting if and only if M is R-liftin...

It is proven that a ring R is δ-semiperfect if and only if every right R-module is (amply) cofinitely δ-supplemented. Mathematics Subject Classification: 16L30, 16E50

The system Galactica of free access is supplemented module for the Coulomb interaction. It is based on a high-precision method for solving differential equations of motion of N charged particles. The paper presents all the theoretical and practical issues required to use this module of system Galactica so that even the beginning researcher could study the motion of particles, atoms and molecules.

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...