Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a graded R-module. The graded classical prime spectrum Cl.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...

abstractacquiring vocabulary, as a significant and challenging part of language learning process, has always been consistent with reading. in this study, the researchers examined the effect of enhanced extensive reading on efl learners’ incidental acquisition of english vocabulary, with specific focus on phrasal verbs. twenty five homogenized participants were selected and divided into two grou...

it is well documented that language learning success or failure is influenced by the affective side of the learner. self-efficacy and anxiety are among the affective factors influencing language learning. this study first explores the relationship between efl learners' self-efficacy in reading comprehension and their reading anxiety. secondly, it explores the relationship between efl learners' ...

understanding the opinions of major role players in education (i.e. teachers, students, and policy makers) on all aspects of learning and teaching is influential to the success of the educational process. the purpose of this study was to investigate efl (english as a foreign language) teachers' views on measuring reading comprehension. a cohort of 50 iranian efl teachers teaching at university,...

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of classical strongly 2-absorbing second submodules modules over rings. A number results concerning these classes their homogeneous components are given.