MATH380 index

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

A:

  • Additive functors: Lecture 18, Section 1.1.
  • Adjoints: Lecture 14, Section 2.1.
  • Algebra: Lecture 3, Section 2.3.
  • Algebra of polynomial functions: Lecture 23, Section 2.1.
  • Algebraic subset: Lecture 23, Section 2.1.
  • Artinian ring: Lecture 3, Section 3.3.
  • Ascending chain: Lecture 5, Section 1.2.
  • Ascending chain terminates: Lecture 5, Section 1.2.

    B:

  • Basic in a module: Lecture 5, Section 0.1.

    C:

  • Category: Lecture 11, Section 1.1.
  • Commutative ring: Lecture 1, Section 1.1.
  • Composition of morphisms: Lecture 11, Section 1.1.
  • Coproducts: Lecture 14, Section 1.

    D:

  • Descending chain: Lecture 6, Section 3.1.
  • Direct product of rings: Lecture 1, Section 1.2.
  • Direct product of modules: Lecture 4, Section 1.1.
  • Direct sum of modules: Lecture 4, Section 1.1.
  • Domain: Lecture 3, Section 1.

    E:

  • Exact functor: Lecture 18, Section 2.2.
  • Exact sequence: Lecture 18, Section 2.1.

    F:

  • Finite algebras: Lecture 21, Section 1.1.
  • Finitely generated algebras: Lecture 6, Section 1.
  • Finitely generated ideals: Lecture 2, Section 3.1.
  • Finitely generated modules: Lecture 4, Section 3.1.
  • Finitely presented modules: Lecture 19, Section 1.2.
  • Flat modules: Lecture 19, Section 1.2.
  • Free module: Lecture 5, Section 0.1.
  • Full subcategory: Lecture 11, Section 1.4.
  • Functor: Lecture 11, Section 2.
  • Functor isomorphism: Lecture 13, Section 1.2.
  • Functor morphism: Lecture 12, Section 2.1.

    G:

  • Generators (a.k.a. spanning set) of a submodule: Lecture 4, Section 3.1

    H:

  • Hom functor (to Sets): Lecture 12, Section 1.

    I:

  • Ideal: Lecture 1, Section 3.1.
  • Integral closure: Lecture 21, Section 2.
  • Integral algebra: Lecture 21, Section 1.1.
  • Integral element: Lecture 21, Section 1.1.
  • Irreducible element (of a ring): Lecture 3, Section 1.2.
  • Irreducible algebraic subset: Lecture 24, Section 1.1.
  • Irreducible component: Lecture 24, Section 1.2.
  • Isomorphism in a category: Lecture 11, Section 1.3.

    L:

  • Left exact functor: Lecture 18, Section 2.2.
  • Local ring: Lecture 10, Section 2.
  • Localization of a module: Lecture 9, Section 2.1.
  • Localization of a ring: Lecture 8, Section 2.
  • Locally free modules: Lecture 19, Section 2.

    M:

  • Maximal ideal: Lecture 2, Section 2.1.
  • Module: Lecture 3, Section 2.1.
  • Module homomorphism: Lecture 3, Section 2.1.
  • Monoid: Lecture 11, Section 1.
  • Morphisms in a category: Lecture 11, Section 1.1.
  • Multiplicative subset: Lecture 8, Section 2.

    N:

  • Noetherian module: Lecture 5, Section 1.1.
  • Noetherian ring: Lecture 5, Section 1.1.
  • Normal domain: Lecture 22, Section 1.1.
  • Normalization of a domain: Lecture 22, Section 1.1.

    O:

  • Objects in a category: Lecture 11, Section 1.1.
  • Objects representing functors: Lecture 13, Section 2.
  • Opposite category: Lecture 11, Section 1.5.

    P:

  • Prime element: Lecture 3, Section 1.1.
  • Prime ideal: Lecture 3, Section 1.1.
  • Principal ideal: Lecture 2, Section 1.2.
  • Principal ideal domain: Lecture 6, Section 4.
  • Products of categories: Lecture 11, Section 1.5.
  • Product of ideals: Lecture 2, Section 1.
  • Porduct of objects: Lecture 13, Section 3.
  • Projective module: Lecture 5, Section 0.2.

    Q:

  • Quotient ring: Lecture 1, Section 3.2.
  • Quotient module: Lecture 1, Section 2.3.

    R:

  • Radical of an ideal: Lecture 2, Section 1.
  • Reducible algebraic subset: Lecture 24, Section 1.1
  • Representing object: Lecture 13, Section 2.
  • Right exact functor: Lecture 18, Section 2.2.
  • Ring : Lecture 1, Section 1.1.
  • Ring homomorphism : Lecture 1, Section 2.
  • Ring of algebraic integers : Lecture 21, Section 2.
  • Ring of polynomials : Lecture 1, Section 1.2.

    S:

  • Short exact sequence (SES): Lecture 18, Section 2.1.
  • Subcategory: Lecture 11, Section 1.4.
  • Submodule: Lecture 4, Section 2.1.
  • Subring: Lecture 1, Section 1.2.
  • Sum of ideals: Lecture 2, Section 1.

    T:

  • Tensor monomials: Lecture 15, Section 2.4.
  • Tensor product of algebras: Lecture 17, Section 2.1.
  • Tensor product of modules: Lecture 15, Section 1.1.

    U:

  • Unit morphism: Lecture 11, Section 1.1.

    V:

  • Vanishing ideal: Lecture 23, Section 2.1.

    Z:

  • Zero divisor: Lecture 3, Section 1.1.