Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.

his study aims to determine most stable isobar from some isobaric elements with mass number (A= 50-65 & 180-195). This aim achieved by, firstly: plot mass parabolas for these isobaric family, second: calculated the atomic number for most stable isobar (ZA) value. To plot the mass parabola, the binding energy (B.E) calculated from semi empirical formula for these isobars. The mass number (A) plotted as a function to the (ZA) for each range; we get a linear relationship between them. An empirical formula for the most stable isobar has been developed from this linear dependence. From the results, we can see that mass parabolas for isobaric elements with odd mass number (A) are different from the mass parabolas of even mass number (A) isobars,

In thisˑ paperˑ, we apply the notion ofˑ intuitionisticˑ fuzzyˑ n-fold KU-ideal of KU-algebra. Some types of ideals such as intuitionistic fuzzy KU-ideal, intuitionisticˑ fuzzy closed idealˑ and intuitionistic fuzzy n-fold KU-ideal are studied. Also, the relations between intuitionistic fuzzy n-fold KU-ideal and intuitionistic fuzzy KU-ideal are discussed. Furthermore, aˑ fewˑ results of intuitionisticˑ fuzzyˑ n-ˑfold KU-ideals of a KU-algebra underˑ homomorphismˑ are discussed.

An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.

The study of homomorphism and Cartesian product is one of the most important mathematical tools that preserve algebraic structures. In this work, a new definition of the concept of a cubic bipolar-ideal under homomorphism in a TM-algebra is introduced. Some important theorems are presented. The notion of Cartesian product for cubic bipolar-ideals and cubic bipolar T-ideals is studied. Also, several properties of the Cartesian product for cubic bipolar-ideals are investigated. Furthermore, the level subsets of the Cartesian product of two cubic bipolar-ideals are defined.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.