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