Preferred Language
Articles
/
vxZ6s4oBVTCNdQwC1KOX
Essential T-small quasi-Dedekind modules
...Show More Authors
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> <sub>ET</sub>M), Then M is called (ET-small Q-D-M). We illustrate them by some examples and discuss some of the basic properties of this types of modules and we present some relationships between this types of modules and other modules such as, T-hollow modules and T-generalized hopfian (T-gH ) modules.</p>
Scopus Crossref
View Publication
Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
T-Small Quasi-Dedekind modules
...Show More Authors
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
View Publication
Scopus Crossref
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Quasi-Small Prime Modules
...Show More Authors
Abstract<p>Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.</p>
Scopus (1)
Crossref (1)
Scopus Crossref
Publication Date
Tue Mar 01 2022
Journal Name
Full Text Book Of Minar Congress4
RELATIONSHIP OF ESSENTIALLY SEMISMALL QUASI-DEDEKIND MODULES WITH SCALAR AND MULTIPLICATION MODULES
...Show More Authors

Let R be a ring with 1 and W is a left Module over R. A Submodule D of an R-Module W is small in W(D ≪ W) if whenever a Submodule V of W s.t W = D + V then V = W. A proper Submodule Y of an R-Module W is semismall in W(Y ≪_S W) if Y = 0 or Y/F ≪ W/F ∀ nonzero Submodules F of Y. A Submodule U of an R-Module E is essentially semismall(U ≪es E), if for every non zero semismall Submodule V of E, V∩U ≠ 0. An R-Module E is essentially semismall quasi-Dedekind(ESSQD) if Hom(E/W, E) = 0 ∀ W ≪es E. A ring R is ESSQD if R is an ESSQD R-Module. An R-Module E is a scalar R-Module if, ∀ , ∃ s.t V(e) = ze ∀ . In this paper, we study the relationship between ESSQD Modules with scalar and multiplication Modules. We show that

... Show More
View Publication
Crossref
Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Semi-Small Compressible Modules and Semi-Small Retractable Modules
...Show More Authors

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 More
Crossref
Publication Date
Wed Sep 01 2021
Journal Name
Baghdad Science Journal
Stable Semisimple Modules, Stable t- Semisimple Modules and Strongly Stable t-Semisimple Modules
...Show More Authors

        Throughout this paper, three concepts are introduced namely stable semisimple modules, stable t-semisimple modules and strongly stable t-semisimple. Many features co-related with these concepts are presented. Also many connections between these concepts are given. Moreover several relationships between these classes of modules and other co-related classes and other related concepts are introduced.

View Publication Preview PDF
Scopus Clarivate Crossref
Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
E-small prime sub-modules and e-small prime modules
...Show More Authors

Scopus Crossref
Publication Date
Sat Jan 01 2011
Journal Name
Al- Mustansiriya J. Sci
Rationally Extending Modules and Strongly Quasi-Monoform Modules
...Show More Authors

An R-module M is called rationally extending if each submodule of M is rational in a direct summand of M. In this paper we study this class of modules which is contained in the class of extending modules, Also we consider the class of strongly quasi-monoform modules, an R-module M is called strongly quasi-monoform if every nonzero proper submodule of M is quasi-invertible relative to some direct summand of M. Conditions are investigated to identify between these classes. Several properties are considered for such modules

View Publication Preview PDF
Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Early Childhood Special Education (int-jecse)
(𝝁∗- Essential Lifting Modules)
...Show More Authors

Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
ESSENTIAL T-hollow-lifting module
...Show More Authors
Abstract<p>Let M be a R-module, where R be a commutative ring with identity, In this paper, we defined a new kind of module namely ET-hollow lifting module, Let T be a submodule of M, M is called ET-hollow lifting module if for every sub-module H of M with <inline-formula> <tex-math><?CDATA $\frac{M}{H}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mfrac> <mi>M</mi> <mi>H</mi> </mfrac> </mrow> </math></inline-formula></p> ... Show More
View Publication
Scopus (2)
Crossref (1)
Scopus Crossref
Publication Date
Tue Jan 01 2019
Journal Name
Italian Journal Of Pure And Applied Mathematics
Co-small monoform modules
...Show More Authors

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 More
View Publication Preview PDF
Scopus