Lectures related to Maximal ideal

Ring Operations: Ideals and Classes

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

Hilberts Nullstellensatz and Ideals

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

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Ideals and PPCM

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

Ideals and Representations

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

Properties of Euclidean Domains

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Primary Decomposition in Commutative Rings

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

Regular Implicit Functions

Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.

Fractions of Rings

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Rankine Cycles: Basics and Energy Balances

Covers the basic concept of Rankine cycles, energy balances, improvements, and limitations.

Local Rings and Residues

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

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.

Prime ideals and local rings

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

Dimension Theory of Rings

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

Cyclotomic Extensions: Norms, Ideals, and Primes

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Dedekind Rings: Integral Extensions and Noetherian Rings

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

Irreducible Factors and Noetherian Rings

Discusses irreducible factors in rings and the properties of Noetherian rings.

Polynomials on a Field: Properties and Applications

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.