Question: Let D be an integral domain. Exercise 37, Section 18 showed that (U, ) is a group where U is the set of units of

Let D be an integral domain. Exercise 37, Section 18 showed that (U, ·) is a group where U is the set of units of D. Show that the set D^* - U of non units of D excluding 0 is closed under multiplication. Is this set a group under the multiplication of D?

Data from Exercises 37 Section 18

Show that if U is the collection of all units in a ring (R, +,·)with unity, then (U, ·) is a group.

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