Difference between revisions of "Math 671: Algebra 1."
From MathWiki
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#* Direct and semidirect products | #* Direct and semidirect products | ||
#* Solvable and Nilpotent groups | #* Solvable and Nilpotent groups | ||
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#Ring Theory | #Ring Theory | ||
#* Definitions and Examples | #* Definitions and Examples | ||
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#* Euclidean Domains, PID's and UFD's | #* Euclidean Domains, PID's and UFD's | ||
#* Polynomial Rings | #* Polynomial Rings | ||
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#Module Theory | #Module Theory | ||
#* Definitions and Examples | #* Definitions and Examples | ||
Revision as of 09:33, 20 August 2008
Contents
Catalog Information
Title
Algebra.
Credit Hours
3
Prerequisite
Description
Desired Learning Outcomes
Prerequisites
Minimal learning outcomes
- Group Theory
- Axioms and Examples
- Homomorphisms and Isomorphisms
- Subgroups
- Centralizers and Normalizers
- Cyclic gorups and subgroups
- Quotient Groups
- Lagrange's Theorem
- Isomorphism theorems
- Group Actions
- Permutation Representations
- Cayley's Theorem
- The class equation
- Sylow theorems
- Direct and semidirect products
- Solvable and Nilpotent groups
- Ring Theory
- Definitions and Examples
- Homomorphisms and quotient rings
- Ideals
- Rings of fractions
- Chinese remainder theorem
- Euclidean Domains, PID's and UFD's
- Polynomial Rings
- Module Theory
- Definitions and Examples
- Quotient modules and homomorphisms
- Direct sums
- Free Modules
- Tensor Products
- Exact Sequences
- Projectives, Injectives, Flats
