Abstract
This chapter is a brief introduction to the extensive applications of homological algebra to ring theory and algebraic geometry. We define various dimensions, use them in polynomial rings and separable algebras, and in the Hilbert theorem on syzygies. Subsequent chapters are independent of this material, except for the description (§ 3) of Ext and Tor for algebras and the direct product and ground ring extensions for algebras.
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© 1995 Springer-Verlag Berlin Heidelberg
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Mac Lane, S. (1995). Dimension. In: Homology. Classics in Mathematics, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-62029-4_8
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DOI: https://doi.org/10.1007/978-3-642-62029-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58662-3
Online ISBN: 978-3-642-62029-4
eBook Packages: Springer Book Archive