Lectures of Pure Mathematics on Algebra Analysis and Geometry

The algebraic theories most relevant to analysis are those which are extensions of the theory of rings. It is widely believed that it is the finiteness of combining power of algebraic operations which distinguishes algebra from analysis. For analysis always appears to involve infinite processes. Application of algebra to geometry essentially involves the use of variables, functions, and equations to represent various known or unknown aspects of, for example, geometric figures. To apply algebra in this context, you don't need any new algebra skills, but you do need to have some understanding of geometry and an ability to translate the somewhat abstract ideas of algebra to a more concrete use in geometry. This book has been prepared by adapting the departments of analysis, algebra and geometry on different and current mathematical problems from a mathematical perspective. The book includes 6 book chapters blended with theoretical knowledge. Each chapter consists of abstract lemmas, propositions and theorems in the field of pure mathematics. At the end of each book chapter, conclusions about the subject are presented. In the first chapter, “Semisimple Normal Injective Krasner Hypermodules” are studied in hyperstructure theory. In the second chapter, “On Quasi-Normal Subgroups of Finite Groups” are studied in group theory. In the third chapter, the concept of ss-supplement, which was brought to the literature in module theory, was extended to hypermodules and the concept of “Hyperstructural Approach to SS-Supplements” and its basic algebraic properties were introduced. In the fourth book chapter titled "Compact Embedding and Inclusion Theorems for Weighted Function Spaces with Wavelet Transform", important findings were reached in Weighted Fuction Spaces by using the Wavelet transform. In the study titled “Bilinear Multipliers of Function Spaces with Wigner Transform” which is the fifth chapter, bilinear multipliers in function spaces with wigner transforms were studied and important analysis methods were developed on this subject. The sixth book chapter is the work entitled "On Almost Kenmotsu Manifolds Accepting Nullity Restrictions”. In this section, appropriate methods have been developed and classes that will enrich manifold theory have been defined.

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