Let (R, +, ×) be a system satisfying all axioms of a ring with identity, except possibly a + b = b + a. Show that a + b = b + a for all a, b ∈ R, so R is indeed a ring
1
Expert's answer
2012-10-17T09:18:09-0400
By the two distributive laws, we have (a + b)(1 + 1) = a(1 + 1) + b(1 + 1) = a + a + b + b, (a + b)(1 + 1) = (a + b)1 + (a + b)1 = a + b + a + b. Using the additive group laws, we deduce that a + b = b + a for all a, b ∈ R
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
"assignmentexpert.com" is professional group of people in Math subjects! They did assignments in very high level of mathematical modelling in the best quality. Thanks a lot
Comments
Leave a comment