Results 1 to 10 of about 1,341,218 (213)

Frobenius Local Rings of Length 5 and Index of Nilpotency 3

Mathematics
This paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
doaj   +4 more sources

Stabilizer codes over Frobenius rings [PDF]

2012 IEEE International Symposium on Information Theory Proceedings, 2012
Quantum error-correcting codes over finite fields have been widely studied, but quantum codes over rings have been left largely unexplored. This paper introduces stabilizer codes over finite Frobenius rings and establishes their connection to classical code. Structural properties of stabilizer codes over finite Frobenius rings are established.
Sushma Nadella, A. Klappenecker
semanticscholar   +5 more sources

Frobenius Local Rings of Order p4m [PDF]

Symmetry
Suppose R is a finite commutative local ring, then it is known that R has four positive integers p,n,m,k called the invariants of R, where p is a prime number. This paper investigates the structure and classification up to isomorphism of local rings with residue field Fpm and of length 4.
Nawal Alsarori, Sami Alabiad, Alhanouf Alhomaidhi   +2 more
exaly   +3 more sources

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
semanticscholar   +3 more sources

On Gray Images of Cyclic and Self-Orthogonal Codes over ${\mathbb{F}}_q+u{\mathbb{F}}_q+v{\mathbb{F}}_q$ [PDF]

Entropy
Let p be a prime with p∉{2,5} and let q=pm. This paper studies cyclic and self-orthogonal linear codes of length n over the finite local non-Frobenius ring Rp,u,v=Fq+uFq+vFq, u2=v2=uv=vu=0.
Sami H. Saif, Alhanouf Ali Alhomaidhi
doaj   +2 more sources

A Griesmer bound for linear codes over finite quasi-Frobenius rings [PDF]

Discrete Applied Mathematics, 2003
In this article we give a Griesmer type bound for linear codes over finite quasi-Frobenius rings and consider linear codes over these rings meeting the bound. And we study a geometrical characterization of linear codes over finite chain rings meeting the
Leo Storme, Keisuke Shiromoto
exaly   +3 more sources

Partitions of Frobenius rings induced by the homogeneous weight [PDF]

Advances in Mathematics of Communications, 2013
The values of the homogeneous weight are determined for finite Frobenius rings that are a direct product of local Frobenius rings. This is used to investigate the partition induced by this weight and its dual partition under character-theoretic ...
H. Gluesing-Luerssen
semanticscholar   +3 more sources

On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings) [PDF]

Nagoya Mathematical Journal, 1955
In this paper we study Frobenius algebras and quasi-Frobenius rings with particular emphasis on their cohomological dimensions. For definitions of these cohomological dimensions we refer the reader to Cartan-Eilenberg [3] or Eilenberg [4].
S. Eilenberg, T. Nakayama
semanticscholar   +4 more sources

FP-Injective and Weakly Quasi-Frobenius Rings [PDF]

Journal of Mathematical Sciences, 1999
The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties of both classes of rings are closely related to the embedding of finitely presented modules in fp-flat and free modules, respectively.
G. Garkusha
semanticscholar   +4 more sources

A generalization of quasi-frobenius rings

Journal of Algebra, 1966
B. Osofsky
semanticscholar   +3 more sources