Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

   Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXW for all fully invariant R-submodule X of M, implies XW.         M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.

The aim of the research is to find out the effect of the SPAWN strategy on the life skills of second-intermediate-grade students. This study stage represented the research community within the intermediate and secondary governmental daytime schools affiliated with the Directorate of Education of Diwaniyah. The experiment was applied in Al-Razai Intermediate School on a sample of second-grade intermediate students, including 66 students distributed into two groups: (32) students within the experimental group and (34) students within the control group. The two groups were equivalent with a number of variables (chronological age, intelligence test, previous information test, life skills scale). The results indicated that the two groups were

The current study aims to investigate the second cycle students’ motives for using electronic games in Oman. The sample consisted of (570) students, (346 males and 224 females). The participants completed an open-ended question which was analyzed based on ground theory. The results showed that (46.820%) of the males and (77.678) of the females played electronic games for pleasure, entertainment, and fun. This first category of motivation got the highest percentage of frequency (58.947%). The motive to become a hacker, a popular YouTuber got the lowest percentage (2.280%). Other students’ motives toward playing electronic games included: filling the leisure time, overcoming boredom, feeling adventures, getting science fiction and chal

Let R be an individual left R-module of the same type as W, with W being a ring containing one. W’s submodules N and K should be referred to as N and K, respectively that K ⊆ N ⊆ W if N/K <<_J (D_j (W)+K)/K, Then K is known as the D J-coessential submodule of Nin W as K⊆_ (Rce) N. Coessential submodule is a generalization of this idea. These submodules have certain interesting qualities, such that if a certain condition is met, the homomorphic image of D J- N has a coessential submodule called D J-coessential submodule.

Let be a commutative ring with unity and let be a submodule of anon zero left R-module , is called semiprime if whenever , implies . In this paper we say that is nearly semiprime, if whenever , implies ( ),(in short ),where ( )is the Jacobson radical of . We give many results of this type of submodules.

Abstract

The aim of the current research is to identify the effect of the effective reading strategy on the achievement of second-middle students in biology, as well as the imaginative thinking skills of students. The researcher adopted the experimental design with partial control to achieve the goal of the research. The current research community identified the second-middle students in the government schools of the Baghdad Education Directorate / Rusafa I for the academic year (2021-2022 AD). The Safina Intermediate School for Girls was chosen to be the research sample in the form of intentionally, two classes were randomly selected from a total of four classes, one of them is experimental and the other is con

      In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout this work, we assume that    is a commutative ring with identity and  is a left unitary R- module. A  proper submodule  of  is called a quasi-radical semi prime submodule (for short Q-rad-semiprime), if     for   ,   ,and then  . Where   is the intersection of all prime submodules of .