e*-Essential small submodules and e*-hollow module
Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
ESSENTIAL T-hollow-lifting module
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
(2)
(1)
Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
Publication Date
Tue Nov 30 2021
Journal Name
Journal Of The Indonesian Mathematical Society
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Large-Small submodule and Large-Hollow module
Abstract<p>The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤<sub>e</sub> M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.</p>
(10)
(1)
Publication Date
Sun Mar 01 2009
Journal Name
Baghdad Science Journal
Weak Essential Submodules
Semi-prime submodules
Essential submodules
Uniform modules.
A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.
(1)
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
Annihilator Essential Submodules
Abstract<p>Through this paper R represent a commutative ring with identity and all R-modules are unitary left R-modules. In this work we consider a generalization of the class of essential submodules namely annihilator essential submodules. We study the relation between the submodule and his annihilator and we give some basic properties. Also we introduce the concept of annihilator uniform modules and annihilator maximal submodules.</p>
(3)
Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Weakly Small Smiprime Submodules
Abstract<p>Let <italic>R</italic> be a commutative ring with an identity, and <italic>G</italic> be a unitary left <italic>R</italic>-module. A proper submodule <italic>H</italic> of an <italic>R</italic>-module <italic>G</italic> is called semiprime if whenever <italic>a ∈ R, y ∈ G, n ∈ Z</italic>
<sup>+</sup> and <italic>a<sup>n</sup>y ∈ H</italic>, then <italic>ay ∈ H</italic>. We say that a properi submodule <italic>H</italic> of an <italic>R</italic>-module <italic>G</italic> is a weakly small semiprime, if whenever <ita></ita></p>
... Show More
Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
J-Small Semiprime Submodules
Abstract<p>Let <italic>R</italic> be a commutative ring with identity and <italic>Y</italic> be an unitary <italic>R</italic>-module. We say a non-zero submodule <italic>s</italic> of <italic>Y</italic> is a <italic>J –</italic> small semiprime if and only if for whenever <italic>i</italic> ∈ <italic>R, y ∈ Y,(Y)</italic> is small in <italic>Y</italic> and <italic>i<sup>2</sup>y</italic> ∈ <italic>S</italic> + <italic>Rad (Y)</italic> implies <italic>iy</italic> ∈ <italic>S.</italic> In this paper, we investigate some properties and chara</p>
... Show More
Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Small Semiprime Submodules
Abstract<p>Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.</p>
(6)
(2)
Publication Date
Sun Sep 04 2016
Journal Name
Baghdad Science Journal
Some Results on Weak Essential Submodules
"Semiprime submodule
Essential submodules
Weak essential submodules
Weak uniform modules
Fully semi-semiprime modules and Fully essential* modules."
Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.