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Index Index

\(\N\), Definition

\(\Z\), Definition

\(\Z_m\), Paragraph

associates, Definition

atom, Definition

binary operation, Definition Definition

Bézout’s Identity, Theorem

commutative ring, Definition

commutative ring with identity, Definition

composite (integers), Definition

congruence mod \(I\), Definition

congruence modulo \(m\), Definition

divides (integers), Definition

divides (ring), Definition

Division Algorithm (\(\N\)), Theorem

Division Algorithm (\(\Z\)), Corollary

domain, Definition

equivalence class, Definition

equivalence class, representative of, Definition

equivalence relation, Definition

Euclidean Algorithm, Investigation

factor (integers), Definition

factor (ring), Definition

field, Definition

First Isomorphism Theorem, Theorem

Fundamental Theorem of Algebra, Assemblage

graph (of a function), Exploration

greatest common divisor (\(\Z\)), Definition

greatest common divisor (integral domain), Definition

ideal (maximal), Definition

ideal (prime), Definition

ideal generated by a set, Definition

ideal, edge, Definition

ideal, finitely generated, Definition

induction, Assemblage

integers, Definition

integral domain, Definition

irreducible (polynomial), Exploration

irreducible (ring element), Definition

maximal ideal, Definition

natural numbers, Definition

overring, Definition

prime (integers), Definition

prime ideal, Definition

quotient ring, Theorem

reducible (polynomial), Definition

relation, Definition

ring, Definition

root, Definition

subring, Definition

subring test, Theorem

unique factorization domain (UFD), Definition

unit, Definition

unity, Definition

well-defined statement, Definition

Well-Ordering Principle, Axiom

zero (of a polynomial), Definition

zero divisor, Definition

zero set, Exploration

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