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Modules and Vector Spaces
Modules and Vector Spaces

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... Here f : G × G → L× , and σ(x) denotes the Galois action of σ on x ∈ L. A tedious verification shows that the associativity of the product above imposes the same associativity condition (3) on f as we have seen before. This construction leads to crossed product algebras (L/K, f). Two such algebras ( ...
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< 1 2 3 4 5 6 7 8 9 10 ... 75 >

Polynomial ring

In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of splitting fields, and to the understanding of a linear operator. Many important conjectures involving polynomial rings, such as Serre's problem, have influenced the study of other rings, and have influenced even the definition of other rings, such as group rings and rings of formal power series.A closely related notion is that of the ring of polynomial functions on a vector space.
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