in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

‎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...

0. Introduction 1. Lie Atoms 1.1 Basic notions 1.2 Representations 1.3 Universal enveloping atom 2. Atomic deformation theory 3. Universal deformations 4. The Hitchin symbol 4.1 The definition 4.2 Cohomological formulae 5. Moduli modules revisited 6. Tangent algbera 7. Differential operators 8. Connection algebra 9. Relative deformations over a global base 10.The Atiyah class of a deformation 1...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

Motivation In relevant application fields ontologies are often maintained as huge monolithic collections of axioms in single files, as for some ontologies in the NCBO BioPortal repository4, like the Gene Ontology (∼ 60, 000 axioms). Such representation is not ideal for applications which only require access limited to individual fragments of the ontology. As an example, the reasoning service pr...

Since the beginning of 2022 to date, “Institute Atomic Energy” Branch Republican State Enterprise “National Nuclear Center Republic Kazakhstan” has been updating subsystems control heaters and monitor parameters liquid sodium information-control system EAGLE test-bench. As part this activity, purchased equipment was installed, initial configuration modules expansion baskets made using specializ...