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(d) Let S = (Q, +, ·), the ring where + is addition of rational numbers and · is multiplicaiton of rational numbers. Prove that the ring R defined in (c) is a subring of S. (e) State the Fundamental Theorem of Algebra.

(d) Let S = (Q, +, ·), the ring where + is addition of rational numbers and · is multiplicaiton of rational numbers. Prove that the ring R defined in (c) is a subring of S. (e) State the Fundamental Theorem of Algebra.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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d and e

5. (a) Give the definition of a group. (b) Show that (Q, +) is an abelian group. (c) Let R = (Z, +, ·), the ring where + is addition of integers and · is multiplication of integers. (i) Is there a multiplicative identity in the ring R? If yes, give it, if no explain why not. (ii) Are there units in the ring R? If yes, write down the set of units. If no, explain why not. (d) Let S = (Q, +, ·), the ring where + is addition of rational numbers and · is multiplicaiton of rational numbers. Prove that the ring R defined in (c) is a subring of S. (e) State the Fundamental Theorem of Algebra.
Transcribed Image Text:5. (a) Give the definition of a group. (b) Show that (Q, +) is an abelian group. (c) Let R = (Z, +, ·), the ring where + is addition of integers and · is multiplication of integers. (i) Is there a multiplicative identity in the ring R? If yes, give it, if no explain why not. (ii) Are there units in the ring R? If yes, write down the set of units. If no, explain why not. (d) Let S = (Q, +, ·), the ring where + is addition of rational numbers and · is multiplicaiton of rational numbers. Prove that the ring R defined in (c) is a subring of S. (e) State the Fundamental Theorem of Algebra.
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