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.
A restrictive relative clause (RRC hereafter), which is also known as a defining relative clause, gives essential information about a noun that comes before it: without this clause the sentence wouldn’t make much sense. A RRC can be introduced by that, which, whose, who, or whom. Givon (1993, 1995), Fox (1987), Fox and Thompson (1990) state that a RCC is used for two main functions: grounding and description. When a RRC serves the function of linking the current referent to the preceding utterance in the discourse, it does a grounding function; and when the information coded in a RRC is associated with the prior proposition frame, the RRC does a proposition-linking grounding function. Furthermore, when a RRC is not used to ground a new di
... Show MoreThe purpose of this paper is to investigate the concept of relative quasi-invertible submodules motivated by rational submodules and quasi-invertible submodules. We introduce several properties and characterizations to relative quasi-invertiblity. We further investigate conditions under which identification consider between rationality, essentiality and relative quasi-invertiblity. Finally, we consider quasiinvertiblity relative to certain classes of submodules
In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved
Let be a module over a commutative ring with identity. In this paper we intoduce the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, where a proper submodule of an -module is said to be Strongly Pseudo Nearly Semi-2-Absorbing submodule of if whenever , for implies that either or , this concept is a generalization of 2_Absorbing submodule, semi 2-Absorbing submodule, and strong form of (Nearly–2–Absorbing, Pseudo_2_Absorbing, and Nearly Semi–2–Absorbing) submodules. Several properties characterizations, and examples concerning this new notion are given. We study the relation between Strongly Pseudo Nearly Semei-2-Absorbing submodule and (2_Absorbing, Nearly_2_Absorbing, Pseudo_2_Absorbing, and Nearly S
... Show MoreThe test considers from important methods and tools when we using the evaluation because it is a basic role in diagnosis & classification & motive & selection &guiding &prediction and the problem was formatted in some questions like ( what is physical variables that tall players needs n the game and effect on the game ? what is the tests that measures these variables also the defense rebound variable and is there a references standard specialized in that ?) , the aims of research represented by knowing to some physical abilities for tall players in basketball school and their tests and putting new tests to measure defense rebound to one player and tow tall players also limiting the standards degrees ( modified un following method ) to resul
... Show MoreSuppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that functions as an act over S if and only if functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following, is acting over S if and only if is a module where T is a nilpotent operator, is a
... Show Moreالأثر V بالنسبة إلى sinshT و خواصه قد تم دراسته في هذا البحث حيث تم دراسة علاقة الأثر المخلص والاثر المنتهى التولد والاثر المنفصل وربطها بالمؤثرات المتباينة حيث تم بهنة العلاقات التالية ان الاثر اذا وفقط اذا مقاس في حالة كون المؤثر هو عديم القوة وكذلك في حالة كون المؤثر شامل فان الاثر هو منتهي التولد اي ان الغضاء هو منتهي التولد وايضا تم برهن ان الاثر مخلص لكل مؤثر مقيد وك\لك قد تم التحقق من انه لاي مؤثر مقي
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