In this research, we introduce a small essentially quasi−Dedekind R-module to generalize the term of an essentially quasi.−Dedekind R-module. We also give some of the basic properties and a number of examples that illustrate these properties.
We introduce in this paper, the notion of a 2-quasì-prime module as a generalization of quasi-prime module, we know that a module E over a ring R is called quasi-prime module, if (0) is quasi-prime submodule. Now, we say that a module E over ring R is a 2-quasi-prime module if (0) is 2-quasi-prime submodule, a proper submodule K of E is 2-quasi-prime submodule if whenever , and , then either or .
Many results about these kinds of modules are obtained and proved, also, we will give a characterization of these kinds of modules.
In this paper, we introduce the concept of e-small Projective modules as a generlization of Projective modules.
Let be a commutative ring with an identity and be a unitary -module. We say that a non-zero submodule of is primary if for each with en either or and an -module is a small primary if = for each proper submodule small in. We provided and demonstrated some of the characterizations and features of these types of submodules (modules).
Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.
In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.
he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga
... Show MoreLet R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each f ∈ Hom(N,M), f ≠0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related modules
Let be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compressible module if can be embedded in every nonzero semi-small submodule of . Equivalently, is semi-small compressible module if there exists a monomorphism , , is said to be semi-small retractable module if , for every non-zero semi-small sub module in . Equivalently, is semi-small retractable if there exists a homomorphism whenever . In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible and retractable respectively and give some of their adv
... Show MoreLet be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compressible module if can be embedded in every nonzero semi-small submodule of . Equivalently, is semi-small compressible module if there exists a monomorphism , , is said to be semi-small retractable module if , for every non-zero semi-small sub module in . Equivalently, is semi-small retractable if there exists a homomorphism whenever .
In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible and retractable respectively and give some of
... Show MoreLet be a commutative ring with 1 and be left unitary . In this papers we introduced and studied concept P-small compressible (An is said to be P-small compressible if can be embedded in every of it is nonzero P-small submodule of . Equivalently, is P-small compressible if there exists a monomorphism , , is said to be P-small retractable if , for every non-zero P-small submodule of . Equivalently, is P-small retractable if there exists a homomorphism whenever as a generalization of compressible and retractable respectively and give some of their advantages characterizations and examples.