Syllabus For The Subject ALGEBRA-1

UNIT - 01

DEFINITION OF A GROUP - EXAMPLES OF GROUP - SOME PRELIMINARY LEMMAS.

UNIT - 02

SUB GROUPS - A COUNTING PRINCIPLE - NORMAL SUB GROUPS AND QUOTIENT

GROUPS.

UNIT - 03

HOMOMARPHISMS.

UNIT - 04

AUTO - MORPHISMS.

UNIT - 05

CAYLEYS `S THEORM - PERMUTATION GROUPS.

UNIT - 06

ANOLNES COUNTING PRINCIPLE AND AYLOUC`S THEORM.

UNIT - 07

DEFINITION AND EXAMPLES OF RING - SOME SPECIAL CLASSES OF RINGS.

UNIT - 08

HOMOMARPHISMS - IDEALS AND QUOTIENT RINGS - THE FIELD OF QUOTIENTS OF AN

INTEGRAL DOMAIN.

UNIT - 09

EUCLIDEAN RINGS - A PARTICULAR EUCLIDEAN RINGS - PLOYNOMIAL RINGS.

UNIT - 10

POLYNOMIALS OVER THE RATIONAL FIELD AND POLYNOMIAL RINGS OVER

COMMUTATIVE RINGS.

UNIT - 11

ELEMENTARY BASIC CONCEPTS OF VECTOR SPACES - LINEAR INDEPENDENCE AND

BASES DUAL SPACES

UNIT - 12

INTER PRODUCT SPACES AND MODULES.

Vinayaka Missions University,Directorate of Distance Education

Salem India

MASTER OF SCIENCE IN MATHEMATICS

1 Yr.

ALGEBRA-1(2030501)