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

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.