Completion of a Field: Algebraic Closure

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Ramification and Structure of Finite Extensions

Explores ramification and structure of finite extensions of Qp, including unramified extensions and Galois properties.

Chinese Remainder Theorem

Explores the Chinese remainder theorem in commutative rings and ideals, demonstrating its applications and relevance in finding unique solutions.

Dedekind Rings and Fractional Ideals

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Chinese Idempotent Constructions and Properties

Explores Chinese idempotent constructions and their properties, including ideals and product characterization.

Dedekind Rings: Integral Extensions and Noetherian Rings

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Primary Decomposition in Rings

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Division Rings and Ideals

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Commutative Algebra: Recollections

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Idempotent Elements and Central Orthogonal

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.