please solve question 3 1) In an Integral domain, Show that the right cancellation law holds2) If (1+x) is an idempotent in Zn; Show that (n-x) is an idempotentScanned with CamScanner3) Given a commutative ring with unity 1 in R; where R is a ring with two maximal ideals M₁ andM₂. Show that i) if le M₁ then M₁ = Rii) M₁ M₂ contains NO non-zero idempotent element.4) Let : Z--------->Z20 such that (x)= 16x ; Show whether is a ring homomorphism or not5) Let D= {0, 1, x1, x2, ....x10} be a finite Integral domain with xi # xj. Show that D is a Field.

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Answered: 3) Given a commutative ring with unity…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 13E

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3) Given a commutative ring with unity 1 in R; where R is a ring with two maximal ideals M₁ and Show that i) if le M₁ then M₁ = R M₂. ii) M₁ M₂ contains NO non-zero idempotent element.