On Prüfer rings as images of Prüfer domains
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- by Monte B. Boisen and Max D. Larsen PDF
- Proc. Amer. Math. Soc. 40 (1973), 87-90 Request permission
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
- Monte B. Boisen Jr. and Max D. Larsen, Prüfer and valuation rings with zero divisors, Pacific J. Math. 40 (1972), 7–12. MR 309921, DOI 10.2140/pjm.1972.40.7
- Malcolm Griffin, Prüfer rings with zero divisors, J. Reine Angew. Math. 239(240) (1969), 55–67. MR 255527, DOI 10.1515/crll.1969.239-240.55
- Max D. Larsen, Prüfer rings of finite character, J. Reine Angew. Math. 247 (1971), 92–96. MR 277522, DOI 10.1515/crll.1971.247.92
- Max. D. Larsen and Paul J. McCarthy, Multiplicative theory of ideals, Pure and Applied Mathematics, Vol. 43, Academic Press, New York-London, 1971. MR 0414528
Additional Information
- © Copyright 1973 American Mathematical Society
- 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