Consider the subset D of M (IR) consisting of the diagonal matrices [9]. a. Prove that D is a subring of M(IR). b. Is D a commutative ring? Prove or disprove. c. Is D a ring with identity? Justify your answer. d. Is D an integral domain? Prove or disprove. e. Is D a field? Prove or disprove.
Consider the subset D of M (IR) consisting of the diagonal matrices [9]. a. Prove that D is a subring of M(IR). b. Is D a commutative ring? Prove or disprove. c. Is D a ring with identity? Justify your answer. d. Is D an integral domain? Prove or disprove. e. Is D a field? Prove or disprove.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 33E: Consider the set S={ [ 0 ],[ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 14 ],[ 16 ] }18. Using addition...
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