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Abstract
Let Rbe a ring with second singular right ideal and second singular left ideal
. Motivated by a result in Zhou (Zhou, Y. (2002). Rings in which certain right ideals are direct summands of annihilators. J. Australian Math. Soc., Ser. A73:335–346 that Ris a two-sided pseudo-Frobenius ring iff Ris a two-sided Kasch ring such that both (
)
R
and
R
(
) are injective, we consider when a right (or two-sided) Kasch ring Rsuch that (
)
R
is injective is right pseudo- Frobenius. Our study leads to a number of new characterizations of one-sided (or two-sided) pseudo-Frobenius rings. Some questions on pseudo-Frobenius rings are listed at the end of the paper.
Acknowledgment
The work of the second author is supported by NSERC, Grant OGP 0194196, of Canada.