Krishna's TB Algebra|Edition-1C|Pages-304|Code-1047 (Mathematics Book 14)

✍ Scribed by A.R Vasishtha

• Publisher: Krishna Prakashan Media Pvt Ltd - Since 1942 (A Unit of THE KRISHNA GROUP)
• Year: 2021
• Tongue: English
• Leaves: 299
• Category: Library

✦ Synopsis

SYLLABUS- ALGEBRA, Definition and examples of groups, examples of abelian and non-abelian
groups, the group Zn of integers under addition modulo n and the group U(n) of
units under multiplication modulo n. Cyclic groups from number systems,
complex roots of unity, circle group, the general linear group GLn (n,R), groups
of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle,(iii) a
rectangle, and (iv) a square, the permutation group Sym (n), Group of
quaternions.
Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset
and the commutator subgroup of group, examples of subgroups including the
center of a group.
Cosets, Index of subgroup, Lagrange’s theorem, order of an element, Normal
subgroups: their definition, examples, and characterizations, Quotient groups.
Definition and examples of rings, examples of commutative and non-commutative
rings: rings from number systems, Zn the ring of integers modulo
n, ring of real quaternions, rings of matrices, polynomial rings, and rings of
continuous functions. Subrings and ideals, Integral domains and fields,
examples of fields: Zp, Q, R, and C.

✦ Table of Contents

Algebra Garhwal
Dedication
Preface
Syllabus
Brief Contents
Chp Page Algebra 1
Chp Page Algebra 2
Chapter 1. Groups
Chapter 2. Permutation Group
Chapter 3. Homomorphism and Isomorphism of Groups
Chapter 4. Subgroups, Cosets and Lagrange's Theorem
Chapter 5. Cyclic Groups
Chapter 6. Normal Subgroups
Chapter 7. Rings
Chapter 8. Subrings and Ideals
Chapter 9. Polynomial Rings