Noetherian Rings and Modules
Chain conditions, Hilbert basis theorem, and primary decomposition.
Noetherian Rings and Modules. Chain conditions, Hilbert basis theorem, and primary decomposition.
Foundations and canonical references
The standard treatments of noetherian rings and modules approach the subject from complementary angles. Atiyah, Introduction to Commutative Algebra (1969) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry (1995) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for noetherian rings and modules include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1969Introduction to Commutative Algebraatiyah-1969, macdonald-1969
- textbook · primary · 1995Commutative Algebra with a View Toward Algebraic Geometryeisenbud-1995
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