Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that A≤D and A D'<<_µ D'. The aim of this paper is to introduce properties of µ-lifting modules. Especially, we give characterizations of µ-lifting modules. On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M

The aim of this work is to give the new types for diskcyclic criterion. We also introduced the case if there is an equivalent relation between a diskcyclic operator  and T that satisfies the diskcyclic criterion. Moreover, we discussed the condition that makes T, which satisfies the diskcyclic criterion, a diskcyclic operator

المتغير العشوائي X  له توزيع أسي اذا كان له دالة احتمالية الكثافة بالشكل:

عندما  ، هذه هي الحالة الخاصة لتوزيع كاما.

غالباً جداً ولسبب معقول تأخذ . الحالة الخاصة لـ (1) التي نحصل عليها تسمى بالتوزيع الاسي لمعلمة واحدة.

اذا كانت  ، ، التوزيع في هذه الحالة يسمى التوزيع الاسي القياسي

اما بالنسب

A gamma T_ pure sub-module also the intersection property for gamma T_pure sub-modules have been studied in this action. Different descriptions and discuss some ownership, as Γ-module Z owns the TΓ_pure intersection property if and only if (J2 ΓK ∩ J^2  ΓF)=J^2 Γ(K ∩ F) for each Γ-ideal J and for all TΓ_pure K, and F in Z Q/P is TΓ_pure sub-module in Z/P, if P in Q.

In this note we consider a generalization of the notion of a purely extending
modules, defined using y– closed submodules.
We show that a ring R is purely y – extending if and only if every cyclic nonsingular
R – module is flat. In particular every nonsingular purely y extending ring is
principal flat.

The aim of this paper is to introduces and study the concept of CSO-compact space via the notation of simply-open sets as well as to investigate their relationship to some well known classes of topological spaces and give some of his properties.

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.

A new class of generalized open sets in a topological space, called G-open sets, is introduced and studied. This class contains all semi-open, preopen, b-open and semi-preopen sets. It is proved that the topology generated by G-open sets contains the topology generated by preopen,b-open and semi-preopen sets respectively.