This Lecture note contains the following topics: Prime
ideals and localization, Finite and integral homomorphisms, Noetherian
rings and modules, Associated Primes and primary decomposition, Noether
normalization, Nullstellensatz and the maximal spectrum, Dimension
theory, special cases of rings, Tor and Ext, Flatness, Depth and Cohen
Macaulay rings and Modules, Regular rings and Graded modules.
Author(s): Mircea Mustata,
Department of University of Michigan
This note covers basic notions, Local properties, Integral
dependence, valuations and completions, Noetherian rings and modules,
Dedekind domains, Dimension theory.
This note covers the following topics: Primary
Decomposition, Filtrations and Completions, Dimension Theory, Integral
Extensions, Homological Methods, Depth and Cohen Macaulay Modules,
Injective Modules over Noetherian Rings, Local Cohomology, Applications
and Generalizations.
This Lecture note contains the following topics: Prime
ideals and localization, Finite and integral homomorphisms, Noetherian
rings and modules, Associated Primes and primary decomposition, Noether
normalization, Nullstellensatz and the maximal spectrum, Dimension
theory, special cases of rings, Tor and Ext, Flatness, Depth and Cohen
Macaulay rings and Modules, Regular rings and Graded modules.
Author(s): Mircea Mustata,
Department of University of Michigan
Commutative
algebra is the branch of algebra that studies commutative rings, their ideals,
and modules over such rings. Basic commutative algebra will be explained in this
document.
This
book is a clear, concise, and efficient textbook, aimed at beginners, with a
good selection of topics. Topics covered includes: Rings and Ideals, Radicals,
Filtered Direct Limits, Cayley–Hamilton Theorem, Localization of Rings and
Modules, Krull–Cohen–Seidenberg Theory, Rings and Ideals, Direct Limits,
Filtered direct limit.