Titlebook: Associative Algebras; Richard S. Pierce Textbook 1982 Springer-Verlag New York Inc. 1982 Algebras.Assoziative Algebra.Category theory.Coho

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Cyclic Division Algebras,a major role in the theory of central simple algebras. If is a local field, an algebraic number field, or more generally a global field, then every central division algebra over . is cyclic. This fact will be proved later; it is one of the most profound results in this book.

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Norms, it is natural to look for analogues of the useful ideas in field theory. This chapter is concerned with the counterpart for central simple algebras of the norm of a field extension. These mappings are called reduced norms.

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Division Algebras over Local Fields, discrete valuation, that is, local fields. The most important property of these algebras is that they contain maximal subfields that are unramified extensions of their centers. It follows that all such algebras are cyclic. Moreover, the classification of the unramified extensions of local fields gi

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Division Algebras over Transcendental Fields,ndant information about algebras over local and global fields that was presented in the last two chapters, our knowledge about division algebras over transcendental fields is sparse. The most important result on this subject is Tsen’s Theorem. It will be proved in Section 4. Tsen’s Theorem is a gene

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https://doi.org/10.1007/978-3-030-50086-3 module theory constitutes a good foundation on which to erect the structure of rings and algebras. On the basis of this dictum, we begin our formal development with this chapter on modules. The emphasis is on semisimple modules, since these structures lead to semisimple algebras, the fundamental bu

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