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On monoids of finite real character

Author: Ulrich Krause
Journal: Proc. Amer. Math. Soc. 105 (1989), 546-554
MSC: Primary 20M14; Secondary 13A18
MathSciNet review: 953009
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Abstract: The property of Krull domains, to be determined already by its essential valuations, is extended to a class of monoids of finite real character containing Krull monoids. This is applied to construct a divisor theory for such monoids and also to characterize Krull domains purely multiplicatively as the integral domains for which the multiplicative monoid is a Krull monoid.

References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, Mass., 1972.
  • [2] L. G. Chouinard II, Krull semigroups and divisor class groups, Canad. J. Math. 33 (1981), 1459-1468. MR 645239 (83g:13013)
  • [3] R. Gilmer, Commutative semigroup rings, The University of Chicago Press, Chicago and London, 1984. MR 741678 (85e:20058)
  • [4] K. R. Goodearl, Partially ordered Abelian groups with interpolation, American Mathematical Society, Providence, 1986. MR 845783 (88f:06013)
  • [5] M. Griffin, Families of finite character and essential valuations, Trans. Amer. Math. Soc. 130 (1968), 75-85. MR 0218336 (36:1423)
  • [6] E. Grosswald, Topics from the theory of numbers, Macmillan, New York, 1966. MR 0228408 (37:3989)
  • [7] H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1986. MR 879273 (88h:13001)

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Keywords: Partially ordered groups, essential valuations, divisor theory, Krull monoids, Krull domains
Article copyright: © Copyright 1989 American Mathematical Society

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