In this paper, the concept of soft closed groups is presented using the soft ideal pre-generalized open and soft pre-open, which are -ᶅ- - -closed sets " -closed", Which illustrating several characteristics of these groups.  We also use some games and   -  Separation Axiom, such as (Æ®_0, Ó¼, ᶅ) that use many tables and charts to illustrate this. Also, we put some proposals to study the relationship between these games and give some examples.

Transforming the common normal distribution through the generated Kummer Beta model to the Kummer Beta Generalized Normal Distribution (KBGND) had been achieved. Then, estimating the distribution parameters and hazard function using the MLE method, and improving these estimations by employing the genetic algorithm. Simulation is used by assuming a number of models and different sample sizes. The main finding was that the common maximum likelihood (MLE) method is the best in estimating the parameters of the Kummer Beta Generalized Normal Distribution (KBGND) compared to the common maximum likelihood according to Mean Squares Error (MSE) and Mean squares Error Integral (IMSE) criteria in estimating the hazard function. While the pr

     Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

In previous our research, the concepts of visible submodules and fully visible modules were introduced, and then these two concepts were fuzzified to fuzzy visible submodules and fully fuzzy. The main goal of this paper is to study the relationships between fully fuzzy visible modules and some types of fuzzy modules such as semiprime, prime, quasi, divisible, F-regular, quasi injective, and duo fuzzy modules, where under certain conditions it has been proven that each fully fuzzy visible module is fuzzy duo. In addition, there are many various properties and important results obtained through this research, which have been illustrated. Also, fuzzy Artinian modules and fuzzy fully stable modules have been introduced, and we study the rel

The research is an article that teaches some classes of fully stable Banach - Å modules. By using Unital algebra studies the properties and characterizations of all classes of fully stable Banach - Å modules. All the results are existing, and they've been listed to complete the requested information.