The theory of automorphisms and derivations of associative rings is a direct descendant of the development of classical Galois theory and the theory of invariants. This volume presents a comprehensive overview of the methods and results of that theory, which has been greatly enriched during the last twenty years. Some of the material included appears for the first time. Among the problems discussed in this book are the following: construction of a Galois theory for prime and semiprime rings and its application to domains and free algebras; investigation of the problems of the algebraic dependence of automorphisms and derivations; studies of the fixed rings for finite groups and rings of constants for differential Lie algebras acting on the rings; non-commutative invariants of linear groups; theorems of finite groups acting on modular lattices; actions of Hopf algebras. The monograph is meant for specialists in algebra, but it can also be useful for a wider range of mathematicians. The inclusions in the book of the latest achievements on the structural theory of rings with generalized identities makes it desirable reading for graduate students as well.

This book provides a systemic view on the digital future from the perspectives of various socio-humanitarian sciences: economics, social sciences, pedagogics and law. Presenting selected papers from the multi-disciplinary international conference "Climate changes and economy of the future: global transformation", which was held at Pskov State University (Russia) on November 13-14, 2019, it offers a comprehensive overview of the current problems and the future potential of digital transformations of economic activities. This multidisciplinary book includes the latest research on the opportunities of the digital economy and the social and ecological consequences of its implementation, and as such offers a "road map" for development. It also features scientific and practical recommendations to allow effective management of the digitization process according to the current priorities.

t moi, ... si favait su comment en revenir. One sel'Yice mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e\re of this series."