On quasi-catenary modules

Document Type: Research articles


Islamic Azad University, Mobarakeh Branch Mobarakeh, Iran samira.asgari.a@gmail.com


We call a module M , quasi-catenary if for each pair of quasi-prime submodules K
and L of M with K  L all saturated chains of quasi-prime submodules
of M from K to L have a common finite length. We show that any homomorphic
image of a quasi-catenary module is quasi-catenary. We prove that if M
is a module with following properties: (i) Every quasi-prime submodule of
M has finite quasi-height; (ii) For every pair of K  L of quasi-prime submodules ofM, qheight(L/K
) = qheight(L) q height(K); then M is quasi-catenary.


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  • س. اسگری
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