Unformatted text preview: 20 i and J = h 18 , 30 i . Find a single generator for each of I , J , I + J , I ∩ J , and I · J . (4) Can you ﬁnd examples of ideals I in commutative rings R with the following properties ? (a) I is principal and maximal, (b) I is principal but not prime, (c) I is maximal but not prime, (d) I is maximal but not principal, (e) I is principal and prime but not maximal. (5) Consider the two polynomials f = x 4 + x 3 + 7 and g = x 22. (a) Compute the remainder of f divided by g . (b) Compute the remainder of g divided by the result of part (a). (c) Determine the ideal in Q [ x ] generated by f and g ....
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 Spring '08
 OGUS
 Math, Algebra, Ring, Bernd Sturmfels, Principal ideal domain

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