Dimension Theory
Krull dimension, regular local rings, and depth.
Dimension Theory. Krull dimension, regular local rings, and depth.
Foundations and canonical references
The standard treatments of dimension theory approach the subject from complementary angles. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry (1995) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Matsumura, Commutative Ring Theory (1989) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for dimension theory 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 · 1995Commutative Algebra with a View Toward Algebraic Geometryeisenbud-1995
- textbook · primary · 1989Commutative Ring Theorymatsumura-1989
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