MATH380 index
A B C D E
F G H
I L
M N O
P
Q R S
T
U
V
Z
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.
Basic in a module: Lecture 5, Section 0.1.
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.
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.
Exact functor: Lecture 18, Section 2.2.
Exact sequence: Lecture 18, Section 2.1.
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.
Generators (a.k.a. spanning set) of a submodule: Lecture 4, Section 3.1
Hom functor (to Sets): Lecture 12, Section 1.
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.
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.
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.
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.
Objects in a category: Lecture 11, Section 1.1.
Objects representing functors: Lecture 13, Section 2.
Opposite category: Lecture 11, Section 1.5.
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.
Quotient ring: Lecture 1, Section 3.2.
Quotient module: Lecture 1, Section 2.3.
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.
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.
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.
Unit morphism: Lecture 11, Section 1.1.
Vanishing ideal: Lecture 23, Section 2.1.
Zero divisor: Lecture 3, Section 1.1.