Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

The product  of   rn-paracompact and   rn-strongly  paracompact are briefly disc. ussed.

This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.

Csaszar introduced the concept of generalized topological space and a new open set in a generalized topological space called -preopen in 2002 and 2005, respectively. Definitions of -preinterior and -preclosuer were given. Successively, several studies have appeared to give many generalizations for an open set. The object of our paper is to give a new type of generalization of an open set in a generalized topological space called -semi-p-open set. We present the definition of this set with its equivalent. We give definitions of -semi-p-interior and -semi-p-closure of a set and discuss their properties. Also the properties of -preinterior and -preclosuer are discussed. In addition, we give a new type of continuous function

In this work, HgBa2CaCu2-xSbxO8+δ compounds with (x = 0.2, 0.4, 0.6 and 0.8) have been prepared by the solid-state reaction method. Structural, morphological, and electrical properties were investigated using X-ray diffraction (XRD) and scanning electron microscope (SEM) techniques. Using the 4-probe technique to study the effect of antimony-substitution for Copper on the electrical properties of HgBa2CaCu2-xSbxO8+δ (Hg-1212) phase was investigated by measuring the resistivity as a function of temperature. Results indicate that the addition of antimony (Sb) increases the volume fraction of the phase and changes the superconducting transition temperature Tc of the superconductor to a normal state. The dielectric loss factor and ac

  The aim of this paper is to introduce a new type of proper mappings called semi-p-proper mapping by using semi-p-open sets, which is weaker than the proper mapping. Some properties and characterizations of this type of mappings are given.

High temperature superconductors with a nominal composition HgBa2Ca2Cu3O8+δ
for different values of pressure (0.2,0.3, 0.5, 0.6, 0.9, 1.0 & 1.1)GPa were prepared by
a solid state reaction method. It has been found that the samples were semiconductor
P=0.2GPa.while the behavior of the other samples are superconductor in the rang
(80-300) K. Also the transition temperature Tc=143K is the maximum at P is equal to
0.5GPa. X-ray diffraction showed a tetragonal structure with the decreasing of the
lattice constant c with the increasing of the pressure. Also we found an increasing of
the density with the pressure.