## A first course in abstract algebra |

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Abelian group abstract algebra additive group additive subgroup bijection binary operation called Chapter commutative ring complex numbers congruences coprime COROLLARY cosets cyclic group deduce defined definition denoted distinct divisible equation equivalence classes equivalence relation Euclid's algorithm Example EXERCISES fact finite follows fractions function G F[X given greatest common divisor group G group of order group with respect Hence homomorphism of rings ideal implies injection integral domain inverse irreducible factors irreducible polynomial isomorphism l(mod laws of standard let a(X Let F Let G mathematics matrices monic multiplicative group neutral element non-zero elements notation nth roots polynomial a(X positive integers prime number Proof Prove quotient set rational numbers reader real numbers residue classes residue classes modulo right cosets satisfying Similarly standard algebra statement subring subset Suppose surjection symmetric true unary uniquely determined unit write Z/nZ