ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIV, 1 (2005)
p. 25 - 36
On (m, n)-quasi-injective modules
Z. M. Zhu, J. L. Chen and X. X. Zhang
Abstract.
Let $R$ be a ring. For two fixed positive integers $m$ and $n$, an
$R$-module $M$ is called {\it\bfseries $(m,n)$-quasi-injective} if
each $R$-homomorphism from an $n$-generated submodule of
$M^{m}$ to $M$ extends to one from $M^{m}$ to $M$.
It is showed that $M_R$ is $(m,n)$-quasi-injective if and only if the right
$R^{n\times n}$-module $M^{m\times n}$ is principally
quasi-injective. Many properties of $(m,n)$-injective
rings and principally quasi-injective modules are extended to these modules.
Moreover, some properties of
$(m,n)$-quasi-injective Kasch modules are investigated.
In particular, some other well-known
results are also obtained.
Keywords:
(m, n)-quasi-injective modules, Kasch modules.
AMS Subject classification: 16D50, 16D90.
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