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ABSTRACT ALGEBRA

MATH 742
과목 설명

Continuation ofMATH 741. Usually the study of commutative rings and fields. Ring theoretic topics may include: modules over PIDs, Noetherian rings and the Hilbert basis theorem, the Lasker-Noether theorem, the Krull intersection theorem, integrality and the Hilbert Nullstellensatz. Field theoretic topics may include: algebraic extensions, Galois theory, solvability of polynomials and classical constructability problems.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

미보고

개설 시기

미보고

평점
3.6

0.51% 과거 데이터 대비

수료율
100%

3.06% 과거 데이터 대비

A 비율
50%

-20.73% 과거 데이터 대비

학급 규모
54

147.44% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

다음 사이트의 평점순으로 정렬 Rate My Professors

유사 과목

ALGEBRAIC NUMBER THEORY

MATH 748

A rigorous introduction to the arithmetic of number fields; algebraic integers, geometry of numbers, Dirichlet's Unit Theorem, ideal class groups, first case of Fermat's Last Theorem; prime decompositions, Galois automorphisms. Basic graduate algebra courses (e.g.MATH 741and742) are strongly recommended.

SEMINAR-ALGEBRA

MATH 941

Selected topics in Algebra.

ABSTRACT ALGEBRA

MATH 741

Usually a study of finite groups and noncommutative rings. Group theoretic topics may include: permutation groups, Lagrange's theorem, Cauchy's theorem and the Sylow theorems, solvable and nilpotent groups. Ring theoretic topics may include: Artinian rings and modules, the Wedderburn theorems, the Hopkins-Levitzki theorem, the Jacobson radical and density theorem. The basic prerequisite for all advanced graduate courses in algebra. Familiarity with topics in undergraduate algebra (e.g.MATH 541and542) is strongly recommended.

MODERN ALGEBRA

MATH 541

Groups, normal subgroups, Cayley's theorem, rings, ideals, homomorphisms, polynomial rings, abstract vector spaces.

TOPICS IN RING THEORY

MATH 746

Will alternate between commutative and noncommutative ring theory. Commutative topics include localization; local rings; dimension theory; Cohen-Macaulay rings. Noncommutative topics include projective modules; injective modules; flat modules; homological and global dimension; Wedderburn and Goldie rings. Basic graduate algebra courses (e.g.MATH 741and742) are strongly recommended.