Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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- Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a field.(Hint: See Exercise 30.)arrow_forwardProve that if R is a field, then R has no nontrivial ideals.arrow_forward15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .arrow_forward
- Let I be an ideal in a ring R with unity. Prove that if I contains an element a that has a multiplicative inverse, then I=R.arrow_forward8. Prove that the characteristic of a field is either 0 or a prime.arrow_forwarda. If R is a commutative ring with unity, show that the characteristic of R[ x ] is the same as the characteristic of R. b. State the characteristic of Zn[ x ]. c. State the characteristic of Z[ x ].arrow_forward
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