Remarks concerning two quasi-Frobenius rings with isomorphic radicals
نویسندگان
چکیده
منابع مشابه
A Note on Quasi-Frobenius Rings
The Faith-Menal conjecture says that every strongly right Johns ring is QF . The conjecture is also equivalent to say every right noetherian left FP -injective ring is QF . In this short article, we show that the conjecture is true under the condition( a proper generalization of left CS condition) that every nonzero complement left ideal is not small( a left ideal I is called small if for every...
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The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...
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Recently the first writer [l] gave a characterization of quasiFrobenius rings, introduced formerly by the second writer [3], in terms of a condition proposed by K. Shoda, which reads: A ring A satisfying minimum condition and possessing a unit element is a quasi-Frobenius ring if and only if A satisfies the following condition:1 (a) every (A -left-) homomorphism of a left-ideal of A into A may ...
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In the present paper new criteria for classes of FP -injective and weakly quasi-Frobenius rings are given. Properties of both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we describe classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (resp. we...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1961
ISSN: 0386-5991
DOI: 10.2996/kmj/1138844467