Abstract Algebra on the Subject GRE

GRE Math Subject · Axiom Academy

INTRO Abstract Algebra on the Subject GRE Groups, rings, fields, and number theory: roughly 25% of the exam What Algebra Means on the GRE Math Subject Test Abstract algebra and number theory together account for approximately 25% of the 66-question GRE Math Subject Test. That translates to roughly 16-17 questions, making this the second-largest section after calculus. Unlike calculus, where many questions are computational, algebra questions often test conceptual understanding -- knowing definitions, recognizing structure, and applying theorems quickly. The GRE tests algebra at the first-year graduate / advanced undergraduate level. You need fluency with groups, rings, and fields -- but not representation theory, homological algebra, or Galois theory beyond basics. Definitions: groups, subgroups, normal subgroups Cyclic groups, generators, order of elements Homomorphisms, isomorphisms, kernel/image Permutation groups , alternating groups Direct products, classification of finite abelian groups Ring and Field Theory (3-5 questions) Ring axioms, commutative rings, integral domains Ideals (principal, maximal, prime) and quotient rings Field extensions, characteristic of a field Polynomial rings and irreducibility Divisibility, primes, Fundamental Theorem of Arithmetic Euclidean algorithm and Bezout's identity Modular arithmetic and congruences Fermat's Little Theorem and Euler's theorem GRE algebra questions span three difficulty tiers: Tier 1: Definition Recall (Easy, ~40%)

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