In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

The main goal of this paper is to introduce a new class in the category of modules. It is called quasi-invertibility monoform (briefly QI-monoform) modules. This class of modules is a generalization of monoform modules. Various properties and another characterization of QI-monoform modules are investigated. So, we prove that an R-module M is QI-monoform if and only if for each non-zero homomorphism f:M E(M), the kernel of this homomorphism is not quasi-invertible submodule of M. Moreover, the cases under which the QI-monoform module can be monoform are discussed. The relationships between QI-monoform and other related concepts such as semisimple, injective and multiplication modules are studied. We also show that they are proper subclass

The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.

The multiplicity of connotations in any paper does not mean that there is no main objective for that paper and certainly one of these papers is our research the main objective is to introduce a new connotation which is type-2 fuzzy somewhere dense set in general type-2 fuzzy topological space and its relationship with open sets of the connotation type-2 fuzzy set in the same space topology and theories of this connotation.

We introduce in this paper the concept of an approximately pure submodule as a     generalization of a pure submodule, that is defined by Anderson and Fuller. If every submodule of an R-module  is approximately pure, then  is called F-approximately regular. Further, many results about this concept are given.

    Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

The existing investigation explains the consequence of irradiation of violet laser on the structure properties of MawsoniteCu₆Fe₂SnS₈ [CFTS] thin films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser. when the received films were processed by continuous red laser (700 nm) with power (>1000mW) for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time (0,30,45,60,75,90 min) respectively at room temperature.. The XRD diffraction gave polycrysta

In this paper we study the concepts of copure submodules and coregular
modules. Many results related with these concepts are obtained.

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.