Does anyone know how to show the following:

Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that

R = { 0R }.

Thx guys. :)

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- February 21st 2006, 08:32 PMsuedenationAlgebra, Ring theory
Does anyone know how to show the following:

Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that

R = { 0R }.

Thx guys. :) - February 22nd 2006, 02:46 PMThePerfectHackerQuote:

Originally Posted by**suedenation**

But because .

Thus,

.

Thus,

But, because .

Thus,

.

Q.E.D.