On Quasi-Small Prime Modules
(1)
(1)
Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
On Quasi-Small Prime Submodules
Prime submodules
quasi-prime submodules
small prime submodules
quasi- small prime submodules
Let be a commutative ring with identity , and be a unitary (left) R-module. A proper submodule of is said to be quasi- small prime submodule , if whenever with and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.
(2)
(1)
Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
Publication Date
Sat Sep 30 2023
Journal Name
Iraqi Journal Of Science
2-Quasi-prime modules
quasi-prime module
2-quasi-prime module
2-quasi-prime submodule
2-prime module
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.
Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
T-Small Quasi-Dedekind modules
Abstract<p>Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if, <inline-formula>
<tex-math><?CDATA $\forall \,w\,\in En{d}_{R}(Q),\,w\ne 0$?></tex-math>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">
<mrow>
<mo>∀</mo>
<mspace width="0.25em"></mspace>
<mi>w</mi>
<mspace width="0.25em"></mspace>
<mo></mo></mrow></math></inline-formula></p>
... Show More
Publication Date
Fri Jun 30 2023
Journal Name
Iraqi Journal Of Science
Z-Small Quasi-Dedekind Modules
Quasi-Dedekind module
Z-small quasi-Dedekind module
Second singular submodule
In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule of -module is called z-small ( if whenever , then . Also, is called a z-small quasi-Dedekind module if for all implies . We also describe some of their properties and characterizations. Finally, some examples are given.
(1)
Publication Date
Mon Feb 01 2021
Journal Name
Journal Of Physics: Conference Series
Essential T-small quasi-Dedekind modules
Abstract<p>Let M be an R-module, where R be a commutative; ring with identity. In this paper, we defined a new kind of submodules, namely T-small quasi-Dedekind module(T-small Q-D-M) and essential T-small quasi-Dedekind module(ET-small Q-D-M). Let T be a proper submodule of an R-module M, M is called an (T-small Q-D-M) if, for all f ∊ End(M), f ≠ 0, implies <italic>Kerf</italic> is an T-small submodule of M <italic>(Kerf</italic>«<sub>T</sub>
<italic>M)</italic>, if T≠ 0 then T ⊈ <italic>Kerf</italic>. In case <italic>Kerf</italic> is an essential T-small submodule of M <italic>(Kerf <<</italic></p>
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Publication Date
Sun Jul 31 2022
Journal Name
Iraqi Journal Of Science
Small-Essentially Quasi-Dedekind R-Modules
Quasi-Ded. modules
Essentially quasi-Ded. modules
K-nonsingular modules
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.
(1)
Publication Date
Sun May 17 2020
Journal Name
Iraqi Journal Of Science
Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules
Essentially small Quasi-Dedekind modules
scalar modules
multiplication modules
Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.
Publication Date
Thu May 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Weakly Quasi-Prime Module
Prime module
quasi-prime module
weakly quasi-prime module.
In this work we shall introduce the concept of weakly quasi-prime modules and give some properties of this type of modules.
Publication Date
Fri Apr 30 2021
Journal Name
Iraqi Journal Of Science
On Small Primary Modules
Primary submodules
Primary modules
Small submodules
Small primary submodule
Small primary 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).