Titlebook: Abstract Algebra; Pierre Antoine Grillet Textbook 2007Latest edition Springer-Verlag New York 2007 Abstract algebra.Galois theory.Lattice.

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Abstract Algebra978-0-387-71568-1Series ISSN 0072-5285 Series E-ISSN 2197-5612

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https://doi.org/10.1007/978-3-319-71422-6a field, albeit limited to fields of algebraic numbers. Steinitz [1910] wrote the first systematic abstract treatment. Today’s approach is basically due to Artin, on whose lectures van der Waerden’s . [1930] is partly based.

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Kathleen M. Higgins,Shakti Maira,Sonia Sikkas, and grew very quickly with the development of algebraic geometry, which consumes vast amounts of it. This chapter contains general properties of ring extensions, Noetherian rings, and prime ideals; takes a look at algebraic integers; and ends with a very minimal introduction to algebraic geometry.

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https://doi.org/10.1007/978-3-319-43893-1d a ring semisimple when it has no nonzero nilpotent ideal and considered in [1907] the particular case of finite-dimensional ring extensions of C. Artin [1927] showed that Wedderburn’s result depends only on the descending chain condition; this gave birth to noncommutative ring theory.