MTH 421 Study Guide - Final Guide: Conjugacy Class, Integral Domain, Normal Subgroup

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12 Oct 2018
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: g s(g/h) is the associated homomorphism, then describe the kernel of . principal ideal domain (pid) normal subgroup euclidean domain. (a b)= (a)^ (b) for all a,b g: let (g, ) and (h,^) be groups. A ______ from g to h is a function : g h such that: homomorphism integral domain subgroup zero divisor: let s r, where r is a ring. We say s is a _____ if: s is an additive subgroup with respect to addition, s is closed under mulitplication zero divisor subgroup subring ideal, let r be a commutative ring with 1 not equal to 0. A _______ of g on x is a function. - (a+b)+c = a+(b+c) for all a,b,c r. - each a r has an additive inverse, denoted -a: a+(-a) = 0 = (-a)+a: r is a semigroup under multiplication: (ab)c = a(bc) for all a,b,c r.

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