Algebra I & II: Course Outline algebra II
Course Outline
Rings:
Definition, examples.
Quadratic integer rings.
Examples of non-commutative rings.
The Hamilton quaternions.
Polynomial rings.
Matrix rings.
Units, zero-divisors, nilpotents, idempotents.
Subrings, Ideals.
Maximal and prime Ideals.
Left, right and two-sided ideals;.
Operations with ideals.
The ideal generated by a set.
Quotient rings. Ring homomorphism.
The isomorphism theorems, applications.
Finitely generated ideals.
Rings of fractions.
Integral Domain:
The Chinese remainder theorem.
Divisibility in integral domains, greatest common divisor, least common multiple.
Euclidean domains.
The Euclidean algorithm.
Principal ideal domains.
Prime and irreducible elements in an integral domain.
Gauss lemma, irreducibility criteria for polynomials.
Unique factorization domains.
Finite fields.
Polynomials in several variables.
Symmetric polynomials.
The fundamental theorem of symmetric polynomials.
Text Books
-
-
A first course in abstract algebra by
Call Number: 512.02 FRAISBN: 9789332519039Publication Date: 2016 -
Related Books
E Books
-
Derek J.S. Robinson
PUBLISHER
De Gruyter
PRINT PUB DATE
2003-01-01 -
Peter J. Cameron
PUBLISHER
OUP Oxford
PRINT PUB DATE
2007-12-13 -
Mohammed Boulagouaz
and Jean-Pierre Tignol
PUBLISHER
CRC Press
PRINT PUB DATE
1999-11-09 -
Mary Hansen
PUBLISHER
Cengage Learning PTR
PRINT PUB DATE
2014-06-18 -
W.J. Wickless
PUBLISHER
Taylor and Francis
PRINT PUB DATE
2004-02-01 -
S. S. Abhyankar
PUBLISHER
World Scientific Publishing Co Pte Ltd
PRINT PUB DATE
2014-05-14 -
Richard C. Penney
PUBLISHER
John Wiley & Sons, Incorporated
PRINT PUB DATE
2015-10-21