Titlebook: Automorphisms and Derivations of Associative Rings; V. K. Kharchenko Book 1991 Springer Science+Business Media Dordrecht 1991 Galois group

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On Algebraic Independence of Automorphisms and Derivations, the problem of algebraic dependence of automorphisms is of importance in a noncommutative situation as well. A simple example that follows shows that from a common point of view automorphisms can be algebraically (and even linearly) dependent.

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The Galois Theory of Prime Rings (The Case of Derivations),a . of its derivations. If the characteristic of a ring is equal to zero, then constants of finite-dimensional Lie algebras are related, but weakly, with the basic ring. Let, for instance, be a free algebra with no unit. Let us consider a derivations μ, such that . = ., . = .. Then its derivation ha

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Applications, not interrelated but they are in this or that way associated with the same basic topics: free algebras, non-commutative invariants, radicals, Goldie rings, rings of quotients, Noetherian rings, etc. It is clearly impossible to try to give a closed presentation of such a wide range of material withi

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Mathematics and its Applicationshttp://image.papertrans.cn/b/image/166634.jpg

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Countermand

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https://doi.org/10.1007/978-94-015-0657-1 the problem of algebraic dependence of automorphisms is of importance in a noncommutative situation as well. A simple example that follows shows that from a common point of view automorphisms can be algebraically (and even linearly) dependent.

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https://doi.org/10.1007/978-94-015-0657-1The contribution of the Galois theory for a class of rings is commonly understood as a proof of the principal correspondence theorem of definite types of finite (or reduced-finite) groups of automorphisms and those of subrings from a given class.

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The Galois Theory of Prime Rings,The contribution of the Galois theory for a class of rings is commonly understood as a proof of the principal correspondence theorem of definite types of finite (or reduced-finite) groups of automorphisms and those of subrings from a given class.