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On Prüfer rings as images of Prüfer domains


Authors: Monte B. Boisen and Max D. Larsen
Journal: Proc. Amer. Math. Soc. 40 (1973), 87-90
MSC: Primary 13F05
DOI: https://doi.org/10.1090/S0002-9939-1973-0319979-5
MathSciNet review: 0319979
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Abstract: Only commutative rings with unity will be considered in this paper. It is shown that if $ R$ is the homomorphic image of a Prüfer domain, then $ R$ is a Prüfer ring but that the converse is not true in general. It is then shown that a Prüfer ring $ R$ is the homomorphic image of a Prüfer domain if and only if the total quotient ring of $ R$ is the homomorphic image of a Prüfer domain. A class of total quotient rings which satisfy this last condition is then presented.


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

  • [1] Monte B. Boisen, Jr. and Max D. Larsen, Prüfer and valuation rings with zero divisors, Pacific J. Math. 40 (1972), 7-12. MR 0309921 (46:9025)
  • [2] Malcolm Griffin, Prüfer rings with zero divisors, J. Reine Angew. Math. 239/240 (1969), 55-67. MR 41 #188. MR 0255527 (41:188)
  • [3] Max D. Larsen, Prüfer rings of finite character, J. Reine Angew. Math. 247 (1971), 92-96. MR 43 #3255. MR 0277522 (43:3255)
  • [4] Max D. Larsen, and Paul J. McCarthy, Multiplicative theory of ideals, Academic Press, New York, 1971. MR 0414528 (54:2629)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0319979-5
Article copyright: © Copyright 1973 American Mathematical Society

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