Let â„› be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z_+, either rⁿℵ=0 or rⁿℵ=rℵ.

In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.

Presents here in the results of comparison between the theoretical equation stated by Huang and Menq and laboratory model tests used to study the bearing capacity of square footing on geogrid-reinforced loose sand by performing model tests. The effects of several parameters were studied in order to study the general behavior of improving the soil by using the geogrid. These parameters include depth of first layer of reinforcement, vertical spacing of reinforcement layers, number of reinforcement layers and types of reinforcement layers The results show that the theoretical equation can be used to estimate the bearing capacity of loose sand.

A class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented 2017, later in 2022, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept

   In this paper, we find the two solutions of two dimensional stochastic Fredholm integral equations contain two gamma processes differ by the parameters in two cases and equal in the third are solved by the Adomain decomposition method. As a result of the solutions probability density functions and their variances at the time t are derived by depending upon the maximum variances of each probability density function with respect to the three cases. The auto covariance and the power spectral density functions are also derived. To indicate which of the three cases is the best, the auto correlation coefficients are calculated.

The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.