Explores the concept of fractions of rings and their uniqueness in ideals and quotients.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.
Covers the concept of ideals in polynomial rings and their properties.
Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.
