Results 1 to 10 of about 15,019 (94)
A Generalization of Quasi-Frobenius Rings [PDF]
Proceedings of the American Mathematical Society, 1969 Let \(R\) be a ring and \(_R\mathcal M\) the category of all left \(R\)-modules. \textit{G. Azumaya} [Nagoya Math. J. 27, 697--708 (1966; Zbl 0144.02303)] proved that if all faithful left \(R\)-modules are generators in \(_R\mathcal M\), \(R\) is left self-injective and a direct sum of indecomposable left ideals having minimal left ideals (cf.
H. Tachikawa
openaire +3 more sources
FP-Injective and Weakly Quasi-Frobenius Rings [PDF]
Journal of Mathematical Sciences, 2002 AMSLatex, 15 ...
G. Garkusha
openaire +4 more sources
On groupoid graded (quasi-)Frobenius rings
Indian Journal of Pure and Applied MathematicsEmil Ilić-Georgijević
exaly +3 more sources
Some results on quasi-Frobenius rings [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2017 Summary: We give some new characterizations of quasi-Frobenius rings by the generalized injectivity of rings. Some characterizations give affirmative answers to some open questions about quasi-Frobenius rings, and some characterizations improve some results on quasi-Frobenius rings.
Zhanmin Zhu
openaire +3 more sources
A Note on Quasi-Frobenius Rings and Ring Epimorphisms
Canadian Mathematical Bulletin, 1969 In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.
H. H. Storrer
openaire +3 more sources
The Structure of Quasi-Frobenius Rings
Canadian Journal of Mathematics, 1974 Utilizing a matrix representation of semiperfect rings by a family of bimodules over local rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic generalized quasi-Frobenius ring is a matrix ring over a cycle of Morita dualities between local rings, and an arbitrary generalized quasi-Frobenius ring is a matrix ring
Bruno J. Müller
openaire +3 more sources
On Almost Quasi-Frobenius Fuzzy Rings
مجلة بغداد للعلوم, 2004 In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.
Baghdad Science Journal
doaj +4 more sources
On the construction of quasi-Frobenius rings
Journal of Algebra, 1973 AbstractA quasi-Frobenius ring (QF ring) is a left Artinian ring R with identity for which the left R-module RR is injective. Since Nakayama [8] introduced the notion of a QF ring, quasi-Frobenius rings have been extensively studied. It is well known that for any QF ring R, both Rn, the ring of n × n matrices over R, and RG, group ring over R for any ...
T. Hannula
openaire +2 more sources