Factorisation in Dedekind Ring

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Page 3 of 4

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Covers the concept of localization and ideals in rings, focusing on extended and contracted ideals, integral extensions, and monic equations.

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Covers the operations in rings, ideals, classes, and quotient rings.

Covers the concept of primary and secondary ideals, focusing on uniqueness and invariance properties.

Covers the interpretation and applications of symbolic powers in algebraic structures, focusing on Krull's Hauptideal Satz and Noetherian rings.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores ideals with finite sets of points and Hilberts Nullstellensatz in algebraic fields.