A submodule N is called rational in M if HomR( M N , E(M))=0, where E(M) is the injective hull of M. Rational submodules have been studied and discussed by many authors such as H.H. Storrer, H. Khabazian, E. Ghashghaei, A. Hajikarimi and A.R. Naghipour, M.S. Abbas and M.A. Ahmed. The main objective of this paper is to give a new class of submodules named P-rational submodules. This class is contained properly in the class of rational submodules. Several properties of this concept are introduced. The relationships between this class of submodules and some other related concepts are discussed such as essential and quasi-invertible submodules. Other characterizations of the P-rational submodule analogous to those which is known in the concept of the rational submodule are given.
The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that .
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In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule of an R-module is called Pr- maximal if ,for any submodule of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule
of an R-module is named near (N-maximal) whensoever is pure submodule of such that then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of is Pr-maximal. A ring is named Pr-ring if whole proper ideal of is a Pr-maximal ideal, we offer the concept pure local (Pr-loc
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The problem of finding the cyclic decomposition (c.d.) for the groups ), where prime upper than 9 is determined in this work. Also, we compute the Artin characters (A.ch.) and Artin indicator (A.ind.) for the same groups, we obtain that after computing the conjugacy classes, cyclic subgroups, the ordinary character table (o.ch.ta.) and the rational valued character table for each group.
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Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.
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Let f and g be a self – maps of a rational exterior space . A natural number m is called a minimal coincidence period of maps f and g if f^m and g^m have a coincidence point which is not coincidence by any earlier iterates. This paper presents a complete description of the set of algebraic coincidence periods for self - maps of a rational exterior space which has rank 2 .
The study aimed to explore the effectiveness of using rational judgment strategy in teaching science to develop scientific thinking for second-grade students. The researcher utilized the quasi-experimental approach based on (the pre/post designing) of two groups: experimental and control. As for tools: a test of scientific thinking prepared by the researcher that proved its verification of their validity and reliability. The test applied on a random sample of (66) students, divided into two groups: (34) experimental, and (32) control. The results showed that the experimental group outperformed the control group in the post-application of the scientific thinking test, In each skill separately, and in the total skills. The study recommende
... Show MoreThe aim of this study is to identify the effectiveness of a rational, emotional, behavioral program in developing self-efficacy to reduce the level of Burnout in 20 teachers of students with autism disorder in Jazan, Saudi Arabia. The proposed program included 12 training sessions. The researcher found that the proposed program has contributed significantly to the development of self-efficacy and reduce the level of Burnout for the targeted subject in this study.
The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .
The concept of a 2-Absorbing submodule is considered as an essential feature in the field of module theory and has many generalizations. This articale discusses the concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules and their relationship to the 2-Absorbing submodule, Quasi-2-Absorbing submodule, Nearly-2-Absorbing submodule, Pseudo-2-Absorbing submodule, and the rest of the other concepts previously studied. The relationship between them has been studied, explaining that the opposite is not true and that under certain conditions the opposite becomes true. This article aims to study this concept and gives the most important propositions, characterizations, remarks, examples, lemmas, and observations related to it. In the en
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