Two characterizations of quasi-Frobenius rings
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 ...
متن کاملStructure of Fp-injective and Weakly Quasi-frobenius Rings
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...
متن کاملTwo characterizations of matrices with the Perron-Frobenius property
Two characterizations of general matrices for which the spectral radius is an eigenvalue and the corresponding eigenvector is either positive or nonnegative are presented. One is a full characterization in terms of the sign of the entries of the spectral projector. In another case, different necessary and sufficient conditions are presented that relate to the classes of the matrix. These charac...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1969
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1969.30.777