determine (with proof or counterexample) which of the 12 ring axioms hold.After that, classify the set (i.e., is your set a ring, commutative ring, ring with identity, integral domain,field).A = {[a b] | a, b, c, d € Z} with matrix addition and matrix multiplication

To determine which of the 12 ring axioms hold for the set A = {a, b, c, d} with matrix addition and…

Answered: determine (with proof or…

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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determine (with proof or counterexample) which of the 12 ring axioms hold. After that, classify the set (i.e., is your set a ring, commutative ring, ring with identity, integral domain, field). A = {[a b] | a, b, c, d € Z} with matrix addition and matrix multiplication