Plane Curves: Singular Points and Multiplicities

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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.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Commutative Algebra: Recollections

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

Curves with Poritsky Property and Liouville Nets

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Ideals and Representations

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

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Ideals and PPCM

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

Irreducible Algebraic Sets

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Projective Geometry: Tangent Lines

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.