Suppose that I is an ideal of J and that J is an ideal of R. Prove that if I has a unity, then I is an ideal of R. (Be careful not to assume that the unity of I is the unity of R. It need not be—see Exercise 2 in Chapter 12.)
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The ring {0, 2, 4, 6, 8} under addition and multiplication modulo 10 has a unity. Find it.
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