| 21. | Any such subring will be a local ring.
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| 22. | There are 2-dimensional, regular local ring, and this makes it possible to describe modules over it.
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| 23. | Cf . the example given at local ring.
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| 24. | A regular local ring is a UFD.
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| 25. | Thus the function field of " X " is just the local ring of its generic point.
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| 26. | A Noetherian local ring is parafactorial if and only if its spectrum is parafactorial along its closed point.
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| 27. | It is a J-2 ring as all Noetherian local rings of dimension at most 1 are J-2 rings.
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| 28. | It leads to an important class of commutative rings, the local rings that have only one maximal ideal.
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| 29. | Local behavior in commutative algebraic geometry is captured by commutative algebra and especially the study of local rings.
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| 30. | Von Neumann regular rings and primitive rings are semiprimitive, however quasi-Frobenius rings and local rings are usually not semiprimitive.
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