1 Attachment(s)

Integral Domains/Algebraic Number Theory - notation/meaning

I am a math hobbyist reading Alaca and Williams "Algebraic Number Theory"

At the bottom of page 9 Alaca & Williams present Theorem 1.3.1 - see attached

The proof begins as follows:

Proof: If a/b $\displaystyle \in $ U(D) then a = bu for some u $\displaystyle \in $ U(D). etc etc (see attached)

[ U(D) is Alaca & WIlliams notation for the set of units of D. The authors do not explain the notation a/b.]

My question is what does he mean by this first statement? What is a/b? is it a divided by b? If so surely 'divides' is not a defined operation in an integral domain? Why start with such a peculiar element as a/b? Can someone clarify for me what is going on here please.

Bernhard.