Kuvempu University Question Papers MSC

Hii sir, I Wants to get the Syllabus And Question Paper of the M.Sc. MATHEMATICS (Previous) Agebra of the Kuvempu University ?

Kuvempu University is a public state university in Shimoga, Karnataka, India. It was established in 1987 by the act of the Karnataka state legislature through amendment No. 28/1976 dated 29 January 1989 under the Karnataka State University Act 1976.


Syllabus And Question Paper of the M.Sc. MATHEMATICS (Previous) Algebra of the Kuvempu University is given below


ALGEBRA (Max marks: 100=75+25. Credits: 05)
UNIT-1: Groups: Definition and examples of groups, Subgroups, abelian groups, cyclic groups, Lagrange’s theorem, normal subgroups and quotient groups,
homomorphism, isomorphism, Cauchy’s theorem for abelian groups, application
of Cauchy’s theorem, automorphism, inner and outer automorphism.

UNIT-2: Permutation Groups: Examples, orbit, cycle, transposition, alternating groups, Cayley’s Theorem, Conjugate class, class equation, Cauchy theorem for finite
groups,

UNIT-3: Sylow’s Theorem and Problems: solvable groups, direct products,
Fundamental theorem on finite abelian groups.

UNIT-4: Rings: Definition and examples of Rings, Integral domain, Field, Characteristic of a Ring, Homomorphism, Kernal, isomorphism, ideals and quotient rings,
maximal ideal, prime ideal, principal ideal ring.

UNIT-5: Euclidean Ring: Definition and examples, greatest common divisor, prime and irreducible elements, unique factorization domain,unique factorization theorem.

UNIT-6: Polynomial Rings: Division Algorithm, irreducible polynomial, primitive
polynomial, Gauss Lemma, Eisentein criterion, polynomial ring over
commutative rings.

UNIT-7: Extention Fields: Definition and example, algebraic extension, transitivity of
algebraic extension, roots of polynomial, Remainder Theorem, Factor theorem.
UNIT-8: Splitting Fields: Degree of Splitting fields, Normal extension, criterion for

polynomial to have a multiple root in any extension field, characteristic of a ring,
separable element, perfect fields.

Question Paper of the M.Sc. MATHEMATICS (Previous) Agebra of the Kuvempu University is given below


M.Sc. MATHEMATICS (Previous) Agebra of the Kuvempu University