**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXIII, 2 (2004)

p. 141 – 149

On injektivity, p-injektivity and YJ-injektivity

R. Yue Chi Ming

**Abstract**.
A sufficient condition is given for a ring to be either
strongly regular or left self-injective regular with non-zero
socle. If $A$ is a left self-injective ring such that the left
annihilator of each element is a cyclic flat left $A$-module, then $A$
is left self-injective regular. Quasi-Frobenius rings are
characterized. A right non-singular, right YJ-injective right FPF
ring is left and right self-injective regular of bounded index.
Right YJ-injective strongly $\pi$-regular rings have nil Jacobson
radical. P.I.-rings whose essential right ideals are idempotent
must be strongly $\pi$-regular. If every essential left ideal of $A$ is
an essential right ideal and every singular right $A$-module is
injective, then $A$ is von Neumann regular, right hereditary.

**Keywords**:
Von Neumann regular, flatness, p-injectivity, P.I.-ring, FPF ring.

**AMS Subject classification:** 16D40, 16D50, 16E50. **
**

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