First Sentence:
Some results and notation that are used throughout the text are collected in this chapter for convenience.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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nonprincipal irreducible character, nonpivotal columns, modules whose annihilators, same free rank, grevlex monomial, invariant factor decomposition, simple radical extensions, universal side divisor, taking homomorphisms, map aug, largest invariant factor, minimal primary decomposition, constructible elements, divisor decomposition, ring under componentwise addition, rational canonical form, left group action, inequivalent extensions, affine algebraic sets, nonisomorphic groups, compatible homomorphisms, known subfields, distinct irreducible characters, complete preimage, localization commutes
Key Phrases - Capitalized Phrases (CAPs):
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Euclidean Domain, Unique Factorization Domain, Fundamental Theorem, Principal Ideal Domain, Sylow's Theorem, Lagrange's Theorem, Zorn's Lemma, Chinese Remainder Theorem, Wedderburn's Theorem, Lattice Isomorphism Theorem, Cauchy's Theorem, Eisenstein's Criterion, Hilbert's Basis Theorem, Burnside's Theorem, Hilbert's Nullstellensatz, Hilbert's Theorem, Maschke's Theorem, Second Isomorphism Theorem, Nakayama's Lemma, Schur's Lemma, Bezout Domain, Shapiro's Lemma, Feit-Thompson Theorem, Frattini's Argument, Noether's Normalization Lemma
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