Nearly integral homomorphisms of commutative rings
1989 ◽
Vol 40
(1)
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pp. 1-12
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A unital homomorphism f: R → T of commutative rings is said to be nearly integral if the induced map R/I → T/IT is integral for each ideal I of R which properly contains ker (f). This concept leads to new characterisations of integral extensions and fields. For instance, if R is not a field, then an inclusion R → T is integral if and only if it is nearly integral and (R, T) is a lying-over pair. It is also proved that each overring extension of an integral domain R is nearly integral if and only if dim (R) ≤ 1 and the integral closure of R is a Prüfer domain. Related properties and examples are also studied.
2012 ◽
Vol 11
(06)
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pp. 1250112
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Keyword(s):
2016 ◽
Vol 15
(06)
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pp. 1650022
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Keyword(s):
1966 ◽
Vol 18
◽
pp. 1024-1030
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Keyword(s):
2021 ◽
Vol ahead-of-print
(ahead-of-print)
◽
1966 ◽
Vol 6
(3)
◽
pp. 351-361
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Keyword(s):
1970 ◽
Vol 40
(1)
◽
pp. 101-120
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1996 ◽
Vol 61
(3)
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pp. 377-380
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Keyword(s):
1982 ◽
Vol 34
(1)
◽
pp. 169-180
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Keyword(s):
2007 ◽
Vol 75
(3)
◽
pp. 417-429
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Keyword(s):
2016 ◽
Vol 95
(1)
◽
pp. 14-21
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