Article
Licensed
Unlicensed
Requires Authentication
Some remarks on quasi-Frobenius rings
-
Zhanmin Zhu
Published/Copyright:
April 14, 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, right JGP-injective ring is quasi-Frobenius, which improves the result on p-injective rings obtained by Jianlong Chen. Moreover, a series of conditions is given under which a left noetherian left mininjective right JGP-injective ring is quasi-Frobenius.
The author wishes to thank the referee for a careful reading of the paper and giving a useful suggestion.
Received: 2013-12-3
Revised: 2014-8-23
Accepted: 2014-9-3
Published Online: 2015-4-14
Published in Print: 2016-3-1
© 2016 by De Gruyter
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- The annihilating-ideal graph of a lattice
- On derivations and commutativity of prime rings with involution
- On the traces of certain classes of permuting mappings in rings
- Measurability properties of certain paradoxical subsets of the real line
- Some classical Tauberian theorems for (C,1,1,1) summable triple sequences
- Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
- Irrationality measures for almost periodic continued fractions
- Elementary volume and measurability properties of additive functions
- On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
- Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity
- Nonlinear iterative algorithms for quasi contraction mapping in modular space
- n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces
- Some remarks on quasi-Frobenius rings
Keywords for this article
Noetherian ring;
YJ-injective ring;
JGP-injective ring;
quasi-Frobenius ring
Articles in the same Issue
- Frontmatter
- The annihilating-ideal graph of a lattice
- On derivations and commutativity of prime rings with involution
- On the traces of certain classes of permuting mappings in rings
- Measurability properties of certain paradoxical subsets of the real line
- Some classical Tauberian theorems for (C,1,1,1) summable triple sequences
- Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
- Irrationality measures for almost periodic continued fractions
- Elementary volume and measurability properties of additive functions
- On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
- Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity
- Nonlinear iterative algorithms for quasi contraction mapping in modular space
- n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces
- Some remarks on quasi-Frobenius rings
