Results 141 to 150 of about 5,492 (174)
Some of the next articles are maybe not open access.
Some characterizations of quasi-Frobenius rings
Bolletino Dell Unione Matematica Italiana, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhanmin Zhu
exaly +2 more sources
On Annihilators and Quasi-Frobenius Rings
Lobachevskii Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOŞAN, MUHAMMET TAMER +2 more
openaire +3 more sources
When Is a Self-Injective Semiperfect Ring Quasi-Frobenius?
Journal of Algebra, 1994 It is shown that a right self-injective semiperfect ring R is quasi-Frobenius if and only if every uniform submodule of any projective right R-module is contained in a finitely generated ...
Clark, J., Vanhuynh, D.
exaly +2 more sources
Graded (quasi-)Frobenius rings
Journal of Algebra, 2023This work presents a study on graded Frobenius algebras from a ring theoretical perspective. To this end, the authors introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and they investigate the structure and representations of such objects.
Dăscălescu, S. +2 more
openaire +2 more sources
Canadian Mathematical Bulletin, 1970
In a recent study of a specific class of quasi-Frobenius rings, Feller has found it useful to introduce the X-rings ([3]). He suggested among others the following topics:(A)Determine the properties of completely indecomposable rings and matrix rings over completely indecomposable rings.(B)Determine the properties of modules over quasi-Frobenius X-rings.
openaire +2 more sources
In a recent study of a specific class of quasi-Frobenius rings, Feller has found it useful to introduce the X-rings ([3]). He suggested among others the following topics:(A)Determine the properties of completely indecomposable rings and matrix rings over completely indecomposable rings.(B)Determine the properties of modules over quasi-Frobenius X-rings.
openaire +2 more sources
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 ...
openaire +3 more sources
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 ...
openaire +3 more sources
New characterizations of quasi-Frobenius rings
Asian-European Journal of Mathematics, 2023In 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 +3 more
openaire +2 more sources
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 +1 more source
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 +1 more source
A note on generalizations of quasi-Frobenius rings
Asian-European Journal of Mathematics, 2016A 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 ...
openaire +1 more source
Some remarks on quasi-Frobenius rings
Georgian Mathematical Journal, 2015Abstract 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,
openaire +2 more sources