21238- Midterm Exam Guide - Comprehensive Notes for the exam ( 48 pages long!)
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6. 1 finitely generated modules over principle ideal domains . 1. 1 logistics: o ce: wean 7121, o ce hours: tuesday 1:30 - 3:00, andrew id: clintonc, grading: 20% homework (graded for completeness), 20% 2 midterms, 40% nal. A module is something for a ring to act on. Informally, modules are the equivalent of group actions for rings. In this course, a ring is not commutative and they don"t necessarily have an identity. Let r = (r, +r, r) be a ring with identity. If m is a unital z-module, we have that. 1 m = m = 2 m = (1 + 1) m = m + m. More generally, for z z, z times z m = m + + m. Thus, the z-action is determined completely by the group (m, +m ). In summary, abelian groups and z-modules are the same thing. Let r = r and consider the euclidean plane r2 = {(x, y) : x, y r}.
