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- Jun 22, 2012

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"The notion of the greatest common divisor of two elements (if it exists)

**can be made precise in**." (my emphasis)

__general rings__Then, the first sentence on page 274 reads as follows: (see attachment - page 274)

"

**Definition.**Let R be a commutative ring and let [TEX] a,b \in R [/TEX] with [TEX] b \ne 0 [/TEX]

... ... "

In this definition D&F go on to define multiple, divisor and greatest common divisor in a commutative ring.

D&F then write the following:

"Note that b|a in a ring if and only if [TEX] a \in (b) [/TEX] if and only if [TEX] (a) \subseteq (b) [/TEX]."

My problem is this - I think D&F should have defined R as a commutative ring

__since proving that [TEX] (a) \subseteq (b) \longrightarrow a \in (b) [/TEX] requires the ring to have an (multiplicative) identity or unity.__

**with identity**Can someone please confirm or clarify this for me?

Peter