Use of the '*' symbol

Question

I am looking at the definition of a 'Euclidean domain', on p.51 of the book 'Polynomial Algorithms in Computer Algebra', by F. Winkler. The definition states :-

"A Euclidean domain (ED) D is an integral domain together with a degree function deg: D* ---> N0, such that:-

a. deg(a.b) >= deg(a) for all a,b elements of D*,

b. (division property) for all a,b elements of D, b not equal to 0, there exists a quotient q and a remainder r in D such that a = q.b + r and (r = 0 or deg(r) < deg(b))"

(Here N0 refers to the set of natural numbers including zero)

My question is simply, what does D* mean? I can find no reference in the book to the use of the asterix. Any idea? I'm assuming its a subfield?

$D^{\ast} = D\setminus{0}$ in this context. Sometimes it refers to the set of units of the ring $D$ — Prahlad Vaidyanathan, Mar 26 '14 at 07:05

score 0 · Answer 1 · answered Mar 26 '14 at 07:13

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Exactly as @Prahlad suggested $D^*$ simply means the Ring without the identity of summation.

I'll give you the definition by M. Artin (Algebra 2nd Edition), so that you have a second reference to work with:

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answered Mar 26 '14 at 07:13

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Many Thanks @Prahlad – Jeremy Watts Mar 26 '14 at 07:30

Use of the '*' symbol

1 Answers1