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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.


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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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