Titlebook: Basic Structures of Modern Algebra; Yuri Bahturin Book 1993 Springer Science+Business Media Dordrecht 1993 Homological algebra.Vector spac

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Commutative Algebra, field of complex numbers . has degree 2 over the field of real numbers . and infinite degree (or to be more exact, no finite degree) over the field of rational numbers .. An important property of finite extensions is expressed by the following lemma.

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Associative Rings,es a precise meaning only by imposing certain definite restrictions. As an example of what is meant we offer the algebra A(.) of all associative non-commuting polynomials in . with coefficients from some field . of zero characteristic. Indeed, such an algebra is primitive.

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Varieties of Algebras, = {.., .., ..} such that .. = ., ..(.) = .., ..(., .) = . (., . ∈ .). It is clear that not each universal algebra with such a set of operations is a group: as a matter of fact, nothing is said about the properties of the operations.

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Lecture Notes in Computer Scienceis happens in the case of an arbitrary set . of pairwise commuting operators, i.e. for a set such that . ? . = 0 for any . ∈ .. The generalization of this result brings a new operation, the commutator of linear operators, and, further, yields the concept of a (linear) Lie algebra.

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Book 1993n 1981 the course "Additional chapters in algebra" replaced the course "Gen- eral algebra" which was founded by A. G. Kurosh (1908-1971), professor and head of the department of higher algebra for a period of several decades. The material of this course formed the basis of A. G. Kurosh‘s well-known

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