Revistes Catalanes amb Accés Obert (RACO)

$\aleph$-products of modules and splitness

F. Lianggui


0 \longrightarrow \prod_{I}^{\aleph}M_{\alpha} \overset{\lambda}{\longrightarrow} \prod_{I}M_{\alpha} \overset{\gamma}{\longrightarrow} \operatorname{Coker}\lambda \longrightarrow 0
be an exact sequence of modules, in which $\aleph$ is an infinite cardinal, $\lambda$ the natural injection and $\gamma$ the natural surjection. In this paper, the conditions are given mainly in the four theorems so that $\lambda$ ($\gamma$ respectively) is split or locally split. Consequently, some known results are generalized. In particular, Theorem 1 of [7] and Theorem 1.6 of [5] are improved.

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