Results 131 to 140 of about 17,562 (171)
, 2018 Some of the next articles are maybe not open access.
Related searches:
Related searches:
Characterization of finite Frobenius rings
Archiv der Mathematik, 2001A ring \(R\) with identity is Frobenius if \(R\) is Artinian and satisfies both \(_R(R/J(R))\cong\text{Soc}(_RR)\) and \((R/J(R))_R\cong\text{Soc}(R_R)\), where \(J(R)\) denotes the Jacobson radical and \(\text{Soc}(-)\) denotes the socles. The author proves that a finite ring \(R\) is Frobenius if \(_R(R/J(R))\cong\text{Soc}(_RR)\).
openaire +4 more sources
Canadian Mathematical Bulletin, 2005
AbstractIt is proved here that a ring R is right pseudo-Frobenius if and only if R is a right Kasch ring such that the second right singular ideal is injective.
Yousif, Mohamed F. +2 more
openaire +2 more sources
AbstractIt is proved here that a ring R is right pseudo-Frobenius if and only if R is a right Kasch ring such that the second right singular ideal is injective.
Yousif, Mohamed F. +2 more
openaire +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
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
Tiled Orders and Frobenius Rings
Mathematical Notes, 2002Let \(R\) be a discrete valuation ring with quotient field \(K\) and \({\mathfrak p}:=\text{Rad\,}R\). For an \(R\)-order \(\Lambda\) in a symmetric \(K\)-algebra \(A\), the \((\Lambda,\Lambda)\)-bimodules \(\Lambda\) and \(\Lambda^*:=\hom_R(\Lambda,R)\) can be regarded as full \(R\)-lattices in \(A\).
Dokuchaev, M. A. +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
Frobenius and Quasi-Frobenius Rings
1999The class of rings that are self-injective (as a left or right module over themselves) has been under close scrutiny by ring theorists. There is a vast literature on the structure of self-injective rings satisfying various other conditions. In a book of limited ambition such as this, it would be difficult to do justice to this extensive literature.
openaire +1 more source