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