Unformatted text preview: F has characteristic 2. 7. Let F be a ﬁeld with unity e , and let R be a subring of F such that e ∈ R and  R  is ﬁnite. Prove that R is an integral domain. Deduce that R is a ﬁeld. 8. Let R be a ring and let I , J ± R . Prove that R / I ∩ J is isomorphic to a subring of R / I × R / J . Hint: deﬁne θ : R → R / I × R / J by θ r = ( I + r , J + r ) . Topics covered since second test Direct sum (product) R × S of rings, integral domains, ﬁelds, characteristic, freshman calculus rule, ring homomorphisms, kernel, ideals, fundamental homomorphism theorem for rings. These are sections 24,25,26,27,38,39. Final on Friday December 9, 10:05 a.m. to 12:05 p.m. in the regular classroom (McBryde 126)....
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This note was uploaded on 01/02/2012 for the course MATH 3124 taught by Professor Parry during the Fall '08 term at Virginia Tech.
 Fall '08
 PARRY
 Math, Algebra

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