MASTER'S EXAM TOPICS IN ABSTRACT ALGEBRA I

THE FOLLOWING ARE THE BASIC KNOWLEDGE A MASTER'S STUDENT SHOULD HAVE CONTROL OF, THIS INCLUDES ALL DEFINIITIONS, IMPORTANT THEOREMS (CERTAINLY NAME BRAND THEOREMS), AND STANDARD EXAMPLES RELATING TO THESE TOPICS.

GROUP THEORY

1) Subgroups

2) Order of elements and groups (LaGrange's Theorem)

3) Cyclic groups

4) Permutation groups

5) Normal subgroups

6) Quotient groups

7) External/Internal direct products/sums

8) Morphisms (Three Isomorphism Theorems)

9) Decomposition of finite Abelian groups

RING THEORY

1) Rings, domains. and fields

2) Subrings and ideals

3) Quotient structure

4) Direct sums/products

5) Morphism

6) Polynomial rings

SOME ACQUAINTANCE WITH OTHER ALGEBRAIC STRUCTURES

1) Vector spaces (including basis and dim)

2) Modules