Let be a ring with identity. Recall that a submodule of a left -module is called strongly essential if for any nonzero subset of , there is such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule of is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules and of that a module has the se-CIP if and only if is strongly essential in implies is strongly essential in . Also, we verify that, a module has the se-CIP if and only if for each se-closed submodule of and for all submodule of , is se-closed in . Finally, some connections and examples are included about (se-CIP)-modules
Let M be an R-module, where R be a commutative;ring with identity. In this paper, we defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of M. Let T be a submodule of M. Let K H M, K is called ET-Coessential of H in M (K⊆ET.ce H), if . A submodule H is called ET- coclosed in M of H has no proper coessential submodule in M, we denote by (K⊆ET.cc H) , that is, K⊆ET.ce H implies that K = H. In our work, we introduce;some properties of ET-coessential and ET-coclosed submodules of M.
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 .
Let
be an
module, and let
be a set, let
be a soft set over
. Then
is said to be a fuzzy soft module over
iff
,
is a fuzzy submodule of
. In this paper, we introduce the concept of fuzzy soft modules over fuzzy soft rings and some of its properties and we define the concepts of quotient module, product and coproduct operations in the category of
modules.
advancing age. The risk of cardiovascular disease in adults is lowest with systolic BP <120 mm Hg and diastolic BP < 80 mm Hg and increases progressively with higher systolic and diastolic blood pressures. Acupuncture (from the Latin word acus, “needle”, and pungere, meaning “prick”) is a technique in which the practitioner inserts fine needles into specific points on the patient’s body. Accupuncture could be used as a nonpharmacological way of controlling high readings of blood pressure among cases with essential hypertension. This study aimed to investigate the effects of acupuncture on essential hypertension.
Patients and Methods: 51 hypertensive patients of both genders and 30 normotensive control subjects were inv
The research is an article that teaches some classes of fully stable Banach - Å modules. By using Unital algebra studies the properties and characterizations of all classes of fully stable Banach - Å modules. All the results are existing, and they've been listed to complete the requested information.
Alloys of Bi2[Te1-x Sex]3 were prepared by melting technique with different values of Se percentage (x=0,0.1,0.3,0.5,0.7,0.9 and 1). Thin films of these alloys were prepared by using thermal evaporation technique under vacuum of 10-5 Torr on glass substrates, deposited at room temperature with a deposition rate (12nm/min) and a constant thickness (450±30 nm). The concentrations of the initial elements Bi, Te and Se in the Bi2 [Te1-x Sex]3 alloys with different values of Se percentage (x), were determined by XRF,The morphological and structural properties were determined by AFM and XRD techniques. AFM images of Bi2[Te1-x Sex]3 thin films show that the average diameter and the average surface roughness inc
... Show MoreThe optical energy gap(Eopt) and the width of the tails of localized states in the band gap (?E) for Se:2%Sb thin films prepared by thermal co-evaporation method as a function of annealing temperature are studied in the photon energy range ( 1 to 5.4)eV.Se2%Sb film was found to be indirect transition with energy gap of (1.973,2.077, 2.096, 2.17) eV at annealing temperature (295,370,445,520)K respectively. The Eopt and ?E of Se:2%Sb films as a function of annealing temperature showed an increase in Eopt and a decrease in ?E with increasing the annealing temperature. This behavior may be related to structural defects and dangling bonds.
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.
Let R be a commutative ring with identity and let Mbe a unitary R-module. We shall say that a proper submodule N of M is nearly S-primary (for short NS-primary), if whenever , , with implies that either or there exists a positive integer n, such that , where is the Jacobson radical of M. In this paper we give some new results of NS-primary submodule. Moreover some characterizations of these classes of submodules are obtained.