This note investigates modules having quasi-injective and duo submodules. We introduce a new generalization of C_1-module. The main method that was adopted in this is how to obtain submodule N M the characteristic Quasi-injective. investigate relationship between pseudo-injective module Quasi-injective property Finally, we anti-hopfian module.

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

This paper addresses the problem of designing a submodule of a given system of communicating timed I/O automata. The problem may be formulated mathematically by the equation (C||X)rA under the constraint IX=In, where C represents the specification of the known part of the system, called the context, A represents the specification of the whole system, X represents the specification of the submod...

The cardinality of the minimal generating set of a module M i.e g(M) plays a very important role in the study of QTAG-Modules. Fuchs [1] mentioned the importance of upper and lower basic subgroups of primary groups. A need was felt to generalize these concepts for modules. An upper basic submodule B of a QTAG-Module M reveals much more information about the structure of M . We find that each ba...

In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. More...

This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this it is relationship to previous generalizationsm especially 2-Absorbing submodule submodule, addition studying most important Propositions, charactarizations Examples. Now research, which considered a continuation definition tha...

This article introduces the concept of S-2-absorbing primary submodule as a generalization 2-absorbing submodule. Let S be multiplicatively closed subset ring R and M an R-module. A proper N is said to if (N :R M) ? = there exists fixed element s such that whenever abm for some a,b m M, then either sam or sbm sab ?(N M). We give several examples, properties characterizations related concept. Mo...