Let R be an associative ring with identity and M be unital non zero R-module. A
submodule N of a module M is called a δ-small submodule of M (briefly N << M )if
N+X=M for any proper submodule X of M with M/X singular, we have
X=M .
In this work,we study the modules which satisfies the ascending chain condition
(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then
we generalize this conditions into the rings , in the last section we get same results
on δ- supplement submodules and we discuss some of these results on this types of
submodules.

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

Let R be a Γ-ring and G be an R_Γ-module. A proper R_Γ-submodule S of G is said to be semiprime R_Γ-submodule if for any ideal I of a Γ-ring R and for any R_Γ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime R_Γ-submodule of R_Γ-module which represents a generalization of semiprime submodules.

Abstract

The research was limited to those whom Imam Abu Dawood

described in his Sunan as weak, so this research does not include

narrators who carried descriptions indicating weakness such as

ignorance or others, nor does it include hadiths that the Imam

described as weak.

The number of narrators whom Imam Abu Dawood described as

weak has reached six narrators, and my methodology was to

mention the words of Imam Abu Dawood, then transfer the

sayings of other advanced scholars, as well as the sayings of

Imam Abu Dawood in his other books, if any, to show the extent

of compatibility between these sayings.

I have reached the following resul

The main purpose of this article is to study the soft LC-spaces as soft spaces in which every soft Lindelöf subset of  is soft closed. Also, we study the weak  forms of soft LC-spaces and we discussed their relationships with soft LC-spaces as well as among themselves.

   The trace elements in the medical herbs play an important role in the treatment of diseases. Well selected herbs samples of Iraqi herbs and collected from local markets. In this study, the concentrations of nine elements Na,K, Zn, Fe ,Co ,Cu ,Ni , Pb and Cd were determined in fourteen kinds herbs common belonging to Matricaria Chamomile Cinnamon,Pimpinella Anisum L., Zea Maize , Anethum Graveolens L., Jeft, Teucrium Polium L., Cagsia Italica,Echium Talicum L.,Ocimum Basilcum L., Galeopsis Sejetum,Nigella Sative L., Cyperus Rotundus L.,Lupinus Jaimehintoniana.The herbs samples were analysed by flameless except Na,K, in flame atomic absorption spectrophotometer in different medical herbs.The results indicated that the Na and K

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 concept and it is relationship to previous generalizationsm especially  2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Abs