Let R be a ring that contains at least two elements. Suppose for each nonzero a
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Let R be a ring that contains at least two elements. Suppose for each nonzero a ∈ R, there exists a unique b ∈ R such that aba = a.
a. Show that R has no divisors of 0.
b. Show that bab = b.
c. Show that R has unity.
d. Show that R is a division ring.
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