On YJ-Injectivity and Annihilators
-
Roger Yue Chi Ming
Abstract
This note contains the following results for a ring A: (1) A is a quasi-Frobenius ring iff A is a left and right YJ-injective, left Noetherian ring whose prime factor rings are right YJ-injective iff every non-zero one-sided ideal of A is the annihilator of a finite subset of elements of A; (2) if A is a right YJ-injective ring such that any finitely generated right ideal is either a maximal right annihilator or a projective right annihilator, then A is either quasi-Frobenius or a right p.p. ring such that every non-zero left ideal of A contains a non-zero idempotent; (3) a commutative YJ-injective Goldie ring is quasi-Frobenius; (4) if the Jacobson radical of A is reduced, every simple left A-module is either YJ-injective or flat and every maximal left ideal of A is either injective or a two-sided ideal of A, then A is either strongly regular or left self-injective regular with non-zero socle.
Heldermann Verlag
Articles in the same Issue
- Interval Oscillation Criteria of Matrix Differential Systems with Damping
- On a Normal of the Distribution of Hyperplane Elements in an Affine Space
- Admissible Diagrams for 𝐺(𝑚, 1, 𝑛)
- Monotonicity and the Asymptotic Estimate of Bleimann Butzer and Hahn Operators Based on Q-Integers
- On Weakly Primary Ideals
- Hardy's Inequality in a Variable Exponent Sobolev Space
- Deciding Linear Disjointness of Finitely Generated Differential Fields
- The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set
- On Linear Conjugation Problems with a Doubly Periodic Jump Line (The Case Of Open Arcs)
- On the Uniqueness Property for Invariant Measures
- Beyond Moser's Conjecture on Grunsky Inequalities
- Set-Theoretic Properties of Schmidt's Ideal
- Composition Operators on 𝑄𝑝 Spaces
- On 𝑚𝑠𝑘-Images of Metric Spaces
- On Nonnegative Solutions of Initial Value Problems for Second Order Linear Functional Differential Equations
- A Note on Fourier Coefficients of Functions of Generalized Wiener Class
- Periodic Solutions of Higher Order Nonlinear Difference Equations Via a Continuation Theorem
- On a Singular Direction of a Meromorphic Function
- Extension of Multiresolution Analysis and the Construction of Orthogonal Multiwavelets
- On YJ-Injectivity and Annihilators
Articles in the same Issue
- Interval Oscillation Criteria of Matrix Differential Systems with Damping
- On a Normal of the Distribution of Hyperplane Elements in an Affine Space
- Admissible Diagrams for 𝐺(𝑚, 1, 𝑛)
- Monotonicity and the Asymptotic Estimate of Bleimann Butzer and Hahn Operators Based on Q-Integers
- On Weakly Primary Ideals
- Hardy's Inequality in a Variable Exponent Sobolev Space
- Deciding Linear Disjointness of Finitely Generated Differential Fields
- The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set
- On Linear Conjugation Problems with a Doubly Periodic Jump Line (The Case Of Open Arcs)
- On the Uniqueness Property for Invariant Measures
- Beyond Moser's Conjecture on Grunsky Inequalities
- Set-Theoretic Properties of Schmidt's Ideal
- Composition Operators on 𝑄𝑝 Spaces
- On 𝑚𝑠𝑘-Images of Metric Spaces
- On Nonnegative Solutions of Initial Value Problems for Second Order Linear Functional Differential Equations
- A Note on Fourier Coefficients of Functions of Generalized Wiener Class
- Periodic Solutions of Higher Order Nonlinear Difference Equations Via a Continuation Theorem
- On a Singular Direction of a Meromorphic Function
- Extension of Multiresolution Analysis and the Construction of Orthogonal Multiwavelets
- On YJ-Injectivity and Annihilators
