1) Let R and S be rings. Show that the cartesian product of setsR x S = {(r, ) |r e R, s €s}with the addition(r, s) + (r', s') := (r +r', s + s')and the multiplication(r, s) · (r', s') := (r - r', s - s')is a ring.

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Answered: 1) Let R and S be rings. Show that the…

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 11E: Assume R is a ring with unity e. Prove Theorem 5.8: If aR has a multiplicative inverse, the...

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1) Let R and S be rings. Show that the cartesian product of sets Rx S = {(r,s) |r € R, s E s} with the addition (r, 8) + (r', s') := (r + r', s + s') and the multiplication (r, s) · (r', s') := (r · r', s · s') is a ring.