A new characterization of Dedekind domains
1986 ◽
Vol 28
(2)
◽
pp. 237-239
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Keyword(s):
Throughout this paper all rings are assumed commutative with identity. Among integral domains, Dedekind domains are characterized by the property that every ideal is a product of prime ideals. For a history and proof of this result the reader is referred to Cohen [2, pp. 31–32]. More generally, Mori [5] has shown that a ring has the property that every ideal is a product of prime ideals if and only if it is a finite direct product of Dedekind domains and special principal ideal rings (SPIRS). Rings with this property are called general Z.P.I.-rings.
1974 ◽
Vol 26
(5)
◽
pp. 1186-1191
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Keyword(s):
2011 ◽
Vol 10
(06)
◽
pp. 1291-1299
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Keyword(s):
2019 ◽
Vol 19
(07)
◽
pp. 2050122
◽
Keyword(s):
2011 ◽
Vol 10
(04)
◽
pp. 701-710
Keyword(s):
1980 ◽
Vol 23
(4)
◽
pp. 457-459
◽
Keyword(s):
1986 ◽
Vol 29
(1)
◽
pp. 25-32
◽
Keyword(s):
1988 ◽
Vol 37
(3)
◽
pp. 353-366
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Keyword(s):