MATH 323 Study Guide - Midterm Guide: Integral Domain, Free Module, Prime Number
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Instructions: you can use the statements we proved in class, or the theorems proved in the textbook, without proof (except the question 4e); but you need to provide complete statements of all the results you quote. Then there is no injective homomorphism from f to m . (b) over an arbitrary integral domain, any submodule of a free module is free: [8 points] recall that for a module m , Ann(m ) = {r r | rm = 0 m m}, and for an ideal i r, Ann(i) = {m m | rm = 0 r i}. Let r be an integral domain, let m be an r-module, and suppose that. Ann(m ) = ij, where i and j are co-maximal ideals in r. prove that. Describe the quotient z[i]/(7). (d) let p > 2 be a prime such that the eld fp contains an element a such that a2 = 1 (in fp).
