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SYLLABUS
Algebra - B.Sc II Year IV Sem (2019-20) (Useful For All Universities of Telangana State)
Unit–I
Groups : Definition and Examples of Groups - Elementary Properties of Groups - Finite Groups - Subgroups - Terminology and Notation - Subgroup Tests - Examples of Subgroups. Cyclic Groups : Properties of Cyclic Groups, Classification of Subgroups Cyclic Groups.
Unit–II
Permutation Groups : Definition and Notation - Cycle Notation - Properties of Permutations - A Check Digit Scheme Based on D5 . Isomorphisms ; Motivation - Definition and Examples - Cayley’s Theorem - Properties of Isomorphism - Automorphisms - Cosets and Lagrange’s Theorem - Properties of Cosets - Lagrange’s Theorem and Consequences - An Application of Cosets to Permutation Groups - The Rotation Group of a Cube and a Soccer Ball.
Unit–III
Normal Subgroups and Factor Groups : Normal Subgroups - Factor Groups - Applications of Factor Groups - Group homomorphisms - Definition and Examples - Properties of Homomorphisms - The First Isomorphism Theorem. Introduction to Rings : Motivation and Definition - Examples of Rings - Properties of Rings - Subrings. Integral Domains : Definition and Examples - Fields - Characteristics of a Ring.
Unit–IV
Ideals and Factor Rings : Ideals - Factor Rings - Prime ideals and maximal ideals. Ring Homomorphisms : Definition and Examples - Properties of Ring - Homomorphisms
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CategoriesArts and Science
Format PDF
TypeeBook