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Mathematics of the USSR-Sbornik, 1977, Volume 31, Issue 2, Pages 249–256
DOI: https://doi.org/10.1070/SM1977v031n02ABEH002301 (Mi sm2683) 		 
Commutative rings with subinjective ideals

L. A. Skornyakov
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DOI: https://doi.org/10.1070/SM1977v031n02ABEH002301
Abstract: An ideal in a commutative ring is called subinjective if it is the homomorphic image of an injective module. It is proved that all ideals in a commutative ring are subinjective if and only if the ring is a direct sum of local rings with this property. Necessary and sufficient conditions are given for all ideals to be subinjective in the local case. In particular, this is the case for self-injective rings whose ideals are linearly ordered, and for local self-injective rings in which the maximal ideal has a nontrivial annihilator.
Bibliography: 7 titles.
Received: 20.05.1976
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1977, Volume 102(144), Number 2, Pages 280–288
Bibliographic databases:
UDC: 519.48
MSC: 13C10
Language: English
Original paper language: Russian
Citation: L. A. Skornyakov, “Commutative rings with subinjective ideals”, Mat. Sb. (N.S.), 102(144):2 (1977), 280–288; Math. USSR-Sb., 31:2 (1977), 249–256
Citation in format AMSBIB
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\by L.~A.~Skornyakov
\paper Commutative rings with subinjective ideals
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 280--288
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\zmath{https://zbmath.org/?q=an:0341.13002|0388.13004}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 249--256
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002301}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977FY72200008}
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  • https://www.mathnet.ru/eng/sm/v144/i2/p280
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    Abstract page:220
    Russian version PDF:74
    English version PDF:9
    References:42
     
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