Throughout this chapter *R* is a commutative integral domain with unity. Such a ring is also called a domain.

If *a* and *b* are nonzero elements in *R*, we say that *b divides a* (or *b* is a *divisor* of *a*) and that *a* is *divisible* by *b* (or *a* is a *multiple* of *b*) if there exists in *R* an element *c* such that *a* = *bc,* and we write *b*|*a* or (mod *b*). Clearly, an element is a unit if and only if *u* is a divisor of 1.

Two elements *a*,*b* in *R* are called *associates* if there exists ...

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