Let k be a ring. Show that the ring A generated over k by x, y with the relations x3 = 0 and xy + yx2 = 1 is the zero ring.
Right multiplying xy + yx2 = 1 by x in A, we get xyx = x. Left multiplying the same equation by x2, we get x2yx2 = x2. Therefore, x2 = x(xyx)x = x3 = 0, and so 1 = xy + yx2 = xy. Left multiplying this by x yields x = x2y = 0 and hence 1 = xy + yx2 = 0 ∈ A, proving that A = (0).
From a young age, our brains develop to the world around us, the environment we live in, and the people…
APPROVED BY CLIENTS
I'm glad I found this service as it has helped me with coursework I don't particularly like doing. I would recommend the response time for errors on completed work to be a bit faster, but other than that I am happy!