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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 4E

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Mark each of the following true or false.
d. As a ring, Z is isomorphic to nZ for all n ≥ 1.
e. The cancellation law holds in any ring that is isomorphic to an integral domain.
f. Every integral domain of characteristic 0 is infinite.
g. The direct product of two integral domains is again an integral domain.
h. A divisor of zero in a commutative ring with unity can have no multiplicative inverse.
i. nZ is a subdomain of Z.
j. Z is a subfield of Q.

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