21. Over a Noetherian integral domain , torsion-free modules are the modules whose only associated prime is 0. 22. Similarly, an integral domain is a Dedekind domain if and only if every divisible module over it is injective. 23. Vieta's formulas are frequently used with polynomials with coefficients in any integral domain " R ". 24. As explained above, neither primitivity nor irreducibility statement of Gauss's lemma is valid over general integral domains . 25. The image of \ varphi is a subring of " L ", and thus an integral domain . 26. The theory is simpler for affine rings, which are integral domains that are finitely generated algebras over a field. 27. Over a general integral domain , we still have one implication : every injective module over an integral domain is divisible. 28. Over a general integral domain, we still have one implication : every injective module over an integral domain is divisible. 29. Pr�fer domains can be characterized as integral domains whose totally ordered abelian group is the value group of some valuation domain. 30. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain .
