a. For a fixed element
b. Give an example of a commutative ring
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ELEMENTS OF MODERN ALGEBRA
- If R1 and R2 are subrings of the ring R, prove that R1R2 is a subring of R.arrow_forward12. Let be a commutative ring with unity. If prove that is an ideal of.arrow_forwardLet 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_forward
- Label each of the following statements as either true or false. Every subring of a ring R is an idea of R.arrow_forward19. Find a specific example of two elements and in a ring such that and .arrow_forwardLet I be the set of all elements of a ring R that have finite additive order. Prove that I is an ideal of R.arrow_forward
- 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set is called the annihilator of in the ring .)arrow_forwardProve that a finite ring R with unity and no zero divisors is a division ring.arrow_forwardExercises Let be an ideal of a ring , and let be a subring of . Prove that is an ideal ofarrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,