Quasi-Frobenius quotient rings of group 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...
متن کاملFp-injective and Weakly Quasi-frobenius Rings
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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Let R be a local ring of prime characteristic. We study the ring of Frobenius operators F(E), where E is the injective hull of the residue field of R. In particular, we examine the finite generation of F(E) over its degree zero component F0(E), and show that F(E) need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of F(E) in good generalit...
متن کاملOn Some Characteristic Properties of Quasi-frobenius and Regular Rings
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...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1975
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700016128