Results 131 to 140 of about 18,020 (162)

New characterizations of quasi-Frobenius rings

Asian-European Journal of Mathematics, 2023
In this paper, we firstly provide several new characterizations of quasi-Frobenius rings by using some generalized injectivity of rings with certain chain conditions. For example, [Formula: see text] a ring [Formula: see text] is quasi-Frobenius if and only if [Formula: see text] is right [Formula: see text], right minfull with ACC on right ...
Thuyet, Le Van, Diallo, Abdoul Djibril, Diop, Papa Cheikhou, Quynh, Truong Cong   +3 more
openaire   +3 more sources

On Quasi-Frobenius Rings

2001
There are three outstanding conjectures about quasi-Frobenius rings: The Faith conjecture that every left perfect, right selfinjective ring is quasi-Frobenius; The FGF-conjecture that every ring for which each finitely generated right module embeds in a free module is quasi-Frobenius; and The Faith-Menal conjecture that every right noetherian ring in ...
W. K. Nicholson, M. F. Yousif
openaire   +2 more sources

A classification of indecomposable Quasi-Frobenius rings I

Communications in Algebra, 2019
This is the first in a series of papers on the classification of indecomposable QF-rings. Our classification is based on the concepts of a nilary ring and the essentiality of the traces of idempotent generated right ideals. Recall that a ring R is called
Gary F Birkenmeier
exaly   +2 more sources

Some remarks on quasi-Frobenius rings

Georgian Mathematical Journal, 2015
Abstract We give some new characterizations of quasi-Frobenius rings by means of YJ-injective rings and JGP-injective rings, respectively. For example, we show that a two-sided YJ-injective right noetherian ring is quasi-Frobenius, which gives an affirmative answer to an open question asked by Roger Yue Chi Ming; a right CF, semiregular,
Zhanmin Zhu
openaire   +3 more sources

A note on generalizations of quasi-Frobenius rings

Asian-European Journal of Mathematics, 2016
A ring [Formula: see text] is called quasi-Frobenius, briefly QF, if [Formula: see text] is right (or left) Artinian and right (or left) self-injective. A ring [Formula: see text] is called right co-Harada if every noncosmall right [Formula: see text]-module contains a nonzero projective direct summand and [Formula: see text] satisfies the ACC on ...
Le Duc Thoang
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Notes on quasi-Frobenius rings

Georgian Mathematical Journal, 2019
Abstract We give some new characterizations of quasi-Frobenius rings. Namely, we prove that for a ring R, the following statements are equivalent: (1) R is a quasi-Frobenius ring, (2) M
Zhanmin Zhu
openaire   +3 more sources

MORE ON QUASI-FROBENIUS RINGS

Mathematics of the USSR-Sbornik, 1973
Let be a ring and its Jacobson radical. Let us set , , and if is a limit ordinal. We call a ring an annihilating ring if the left (right) annihilator of the right (left) annihilator of an arbitrary left (right) ideal is itself. We prove that a ring is quasi-Frobenius if and only if it is a left self-injective annihilating ring and for some ...
L. Skornjakov
openaire   +4 more sources

Quasi-Frobenius Rings and Generalizations QF-3 and QF-1 Rings

Lecture Notes in Mathematics, 1973
Hiroyuki Tachikawa
exaly   +2 more sources

On decomposition of strongly quasi-frobenius rings

Communications in Algebra, 2000
We prove that the Nakayama permutation of a strongly quasi-Frobenius ring gives rise to a ring decomposition of the ring.
Y. Yukimoto
openaire   +2 more sources

A Griesmer Bound for Codes over Finite Quasi-Frobenius Rings

Electronic Notes in Discrete Mathematics, 2001
Keisuke Shiromoto, L Storme
exaly   +2 more sources