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MATH 412 Midterm: MATH 412 Exam 1

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turquoisegnu128

31 Jan 2019

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Part i: true or false (total 20 points: 2 points for correct answer, -1 for incorrect). The ring of continuous real-valued functions of the real line is an integral domain. Every subring of a commutative ring is commutative. If r and s are elds, then r s is a eld. An integer is divisible by 99 if and only if it is divisible by both 9 and 11. The map z z sending each integer to its additive inverse is a ring homomorphism. If r is ring with identity 1r, then every non-zero element of r has the form 1r + 1r + A ring r is commutative if and only if (a + b)(a b) = a2 b2 for all a, b r. If two nite rings are isomorphic, they must have the same number of zero-divisors. Let r be a commutative ring with identity.

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