Wieslaw A. Dudek - Böcker

This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations.The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics.The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms.The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications.The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.

This monograph is devoted to various types of algebras of functions with n variables. It is the first complete monograph (in English) on this topic, covering mainly the Russian literature. It is addressed to all algebraists working in the area of universal algebras, semigroup theory, etc. It is also a useful source of information for graduate and PhD students who are starting their research in this area.The book is the first monograph in the English mathematical literature which provides readers with a very systematical study of the notion of Menger algebras, and its generalizations and applications. The results presented here were originally published mostly in the Russian literature: In 2006, the first version of this book was edited in Russian and it is now presented in an extended version, where two new and very important chapters are added. The monograph is a broad survey of unknown or little-known Russian literature on algebras of multiplace functions and presents to the mathematical community a beautiful and strongly developing theory.

It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures.