Let Rbe a ring, and a, b e R.What is the needed condition on R such that the expression (a + b) (a – b) = a² – b² | - ? is true Ris a commutative ring Ris a ring with unity Every nonzero element of R is a unit every element of R is an idempotent

Let Rbe a ring, and a, b e R.What is the needed condition on R such that the expression (a + b) (a – b) = a² – b² | - ? is true Ris a commutative ring Ris a ring with unity Every nonzero element of R is a unit every element of R is an idempotent

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 3TFE

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Question

Let R be a ring, and
a, 6 e R.What is
the needed condition on
R such that the
expression
(a + b) (a – b) = a² – b²
? is true
Ris a commutative ring
Ris a ring with unity
Every nonzero element of R
is a unit
every element of R is an
idempotent

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