MATH380 index

A B C D F G H I L M N O P Q R S Z

A:

  • Algebra (over a commutative ring): Lecture 3, Section 2.3.
  • Algebraic subset: Lecture 14, Section 1.4.
  • Ascending chain (AC) of submodules: Lecture 5, Section 1.2.
  • AC termination: Lecture 5, Section 1.2.
  • Algebra of polynomial functions: Lecture 15, Section 2.
  • Artinian module: Lecture 6, Section 2.1.
  • Artinian ring: Lecture 6, Section 2.3.

    B:

  • Basis of a module: Lecture 4, Section 3.2.

    C:

  • Category: Lecture 16, Section 2.1.
  • Class group: Lecture 13, Section 1.4.
  • Commutative ring: Lecture 1, Section 1.1.

    D:

  • Dedekind domain: Lecture 12, Section 1.1.
  • Descending chain (DC) of submodules: Lecture 6, Section 2.1.
  • DC termination: Lecture 6, Section 2.1.
  • Direct product of modules: Lecture 3, Section 2.4.
  • Direct product of rings: Lecture 1, Section 1.2.
  • Direct sum of modules: Lecture 3, Section 2.4.
  • Domain: Lecture 2, Section 3.

    F:

  • Finite algebra: Lecture 10, Section 2.1.
  • Finitely generated ideals: Lecture 1, Section 3.1.
  • Finitely generated algebras: Lecture 5, Section 2.2.
  • Finitely generated modules: Lecture 4, Section 3.1.
  • Fractional ideal: Lecture 13, Section 1.1
  • Free modules: Lecture 4, Section 3.2.
  • Full subcategory: Lecture 16, Section 2.4.
  • Functor: Lecture 17, Section 1.1.
  • Functor morphism: Lecture 17, Section 2.1.

    G:

  • Generators (a.k.a. spanning set) of a module: Lecture 4, Section 3.2.

    H:

  • Hom module: Lecture 4, Section 1.

    I:

  • Ideal: Lecture 1, Section 3.1.
  • Integral algebra: Lecture 10, Section 2.1.
  • Integral closure: Lecture 11, Section 2.1.
  • Irreducible algebraic subset: Lecture 15, Section 1.1.
  • Irreducible component: Lecture 15, Section 1.2.
  • Irreducible element (of a domain): Lecture 3, Section 1.

    L:

  • Localization of a ring: Lecture 8, Section 2.2.
  • Localization of a module: Lecture 9, Section 2.1.
  • Localization of a module homomorphism: Lecture 9, Section 2.2.

    M:

  • Maximal ideal: Lecture 2, Section 2.1.
  • Module: Lecture 3, Section 2.1.
  • Module homomorphism: Lecture 3, Section 2.1.
  • Monoid: Lecture 16, Section 2.
  • Multiplicative homomorphism: Lecture 8, Section 2.1.

    N:

  • Noetherian module: Lecture 5, Section 1.1.
  • Noetherian ring: Lecture 5, Section 1.1.
  • Normal domain: Lecture 11, Section 2.3.

    O:

  • Opposite category : Lecture 16, Section 2.5.

    P:

  • Prime ideal: Lecture 2, Section 3.
  • Principal ideal: Lecture 1, Section 3.
  • Principal ideal domain: Lecture 6, Section 3.1.
  • Product of categories: Lecture 16, Section 2.5.
  • Product of functors: Lecture 18, Section 2.
  • Product of objects: Lecture 18, Section 2.
  • Product of ideals: Lecture 2, Section 1.
  • Product of ideal and submodule: Lecture 4, Section 2.2.

    Q:

  • Quotient module: Lecture 4, Section 2.2.
  • Quotient ring: Lecture 1, Section 3.2.

    R:

  • Radical ideal: Lecture 14, Section 1.4.
  • Radical of an ideal: Lecture 2, Section 1.
  • Reducible algebraic subset: Lecture 15, Section 1.2.
  • Representable functor: Lecture 18, Section 1.3.
  • Representing object: Lecture 18, Section 1.3.
  • Ring : Lecture 1, Section 1.1.
  • Ring homomorphism : Lecture 1, Section 2.
  • Ring of algebraic integers: Lecture 11, Section 2.2.
  • Ring of polynomials : Lecture 1, Section 1.2.

    S:

  • Small category: Lecture 16, Section 2.3.
  • Subcategory: Lecture 16, Section 2.4.
  • Subring: Lecture 1, Section 1.2.
  • Submodule: Lecture 2, Section 2.1.
  • Sum of ideals: Lecture 2, Section 1.
  • Sum of submodules: Lecture 4, Section 2.2.

    Z:

  • Zero divisor: Lecture 2, Section 3.