A first course in abstract algebra: rings, groups, and fields

Numbers, Polynomials, and Factoring The Natural Numbers The Integers Modular Arithmetic Polynomials with Rational CoefficientsFactorization of PolynomialsSection I in a NutshellRings, Domains, and Fields Rings Subrings and Unity Integral Domains and Fields Ideals Polynomials over a Field Section II in a NutshellRing Homomorphisms and Ideals Ring HomomorphismsThe Kernel Rings of Cosets The Isomorphism Theorem for Rings Maximal and Prime Ideals The Chinese Remainder Theorem Section III in a NutshellGroups Symmetries of Geometric Figures PermutationsAbstract Groups Subgroups Cyclic Groups Section