Let R is ring of real numbers and *, (2)O defind on R^2 as follows, (a, b),A(c, d)ER^2 then (a, b)* (c, d) =(a+c,b+d) and (a, b)0 (c, d) =(ac-bd,ad+bd) , Prove that(R^2, *, 0) is* commutative ring with identity

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Let R is ring of real numbers and *, (2) O defind on R^2 as follows, V (a, b), (c, d)ER^2 then (a, b)* (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, *, O) is * commutative ring with identity

Let R is ring of real numbers and , (2) O defind on R^2 as follows, V (a, b), (c, d)ER^2 then (a, b) (c, d) =(a+c, b+d) and (a, b)0 (c, d) =(ac-bd, ad+bd) , Prove that(R^2, , O) is commutative ring with identity

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 3E: Find all monic irreducible polynomials of degree 2 over Z3.

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Question

Let R is ring of real numbers and *, (2)
O defind on R^2 as follows, (a, b),
A
(c, d)ER^2 then (a, b)* (c, d) =(a+c,
b+d) and (a, b)0 (c, d) =(ac-bd,
ad+bd) , Prove that(R^2, *, 0) is
* commutative ring with identity

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