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Indian Institute of Science Education and Research Bhopal

MTH 602: Algebra II (4)

Extension of rings, integral extensions, going up and going down theorems, integral closure, integral galois extensions

Transcendental extension, transcendence basis, Noether normalization theorem, separable and regular extensions

Algebraic varieties, Hilbert's Nullstellensatz, Spec of a ring

Noetherian (and Artinian) rings and Modules

Matrices and linear maps, determinants, duality, bilinear and quadratic forms

Tensor product, basic properties, bimodules, Flat modules, extension of scalars, Algebras, Graded algebras, Tensor, symmetric and exterior algebras

Suggested Books:

• S. Lang, Algebra, 3rd Edition, Addison Wesley.
• Jacobson, Basic Algebra I and II.
• Birkhoff and McLane, Algebra.
• Dummit and Foote, Abstract Algebra, 2nd Edition, Wiley.

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