Regularity and Noetherian Local Rings

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Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

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

Introduces ample invertible sheaves and their properties in algebraic geometry.

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.