If R is a system satisfying all the conditions for a ring with unit element with possible exception of a + b = b + a, prove that the axiom a + b = b + a must hold in R and that R is thus a ring. (Hint: Expand (a + b)(1 + 1) in two ways.

If R is a system satisfying all the conditions for a ring with unit element with possible exception of a + b = b + a, prove that the axiom a + b = b + a must hold in R and that R is thus a ring. (Hint: Expand (a + b)(1 + 1) in two ways.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 16E: A Boolean ring is a ring in which all elements x satisfy x2=x. Prove that every Boolean ring has...

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