Cyclotomic Extensions: Norms, Ideals, and Primes

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Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Mathematical structures: selected topics

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Dimension Theory of Rings

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

Ring Operations: Ideals and Classes

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

Localization and Ideals

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

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

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.

Ideals and PPCM

Covers the concept of ideals in polynomial rings and their properties.

Prime ideals and local rings

Covers the concept of prime ideals and local rings, emphasizing their importance.

Primary Decomposition in Commutative Rings

Covers primary decomposition in commutative rings and its application in prime ideals.