This exercise shows that every ring R can be enlarged (if necessary) to a ring S with unity, having the same characteristic as R. Let S = R × Z if R has characteristic 0, and R × ℤn if R has characteristic n. Let addition in S be the usual addition by components, and let multiplication be defined by (r1,n1)(r2, n2) = (r1r2 + n1 • r2 + n2 • r1, nl n2)
where n • r has the meaning explained in Section 18.
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