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Q18. Let R be a commutative ring, and let I, J be ideals of R. Define the product IJ as follows: An element x belongs to Î if and only if we can write r =ã1J1 +ãnJn for various il' . . . Ä°n Ð Ð and J1, . . . jn of summands n > 1 depends on x. J. where thenumber (a) Show that IJ is an ideal of R (b) Show that every element of IJ belongs to both I and J (c) In Z, let I -4Z and J 6Z. Find IJ in the form (?)Z. Next, find an integer which is in both I and J, but is not in IJ