M.S. Exam -- Algebra
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
- Subgroups
- Order of elements and groups (LaGrange's Theorem)
- Cyclic groups
- Permutation groups
- Normal subgroups
- Quotient groups
- External/Internal direct products/sums
- Morphisms (Three Isomorphism Theorems)
- Decomposition of finite Abelian groups
RING THEORY
- Rings, domains. and fields
- Subrings and ideals
- Quotient structure
- Direct sums/products
- Morphism
- Polynomial rings
SOME ACQUAINTANCE WITH OTHER ALGEBRAIC STRUCTURES
- Vector spaces (including basis and dim)
- Modules
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