Islamic Azad University, Mobarakeh Branch Mobarakeh, Iran samira.asgari.a@gmail.com
Abstract
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, q−height(L/K ) = q− height(L) − q − height(K); then M is quasi-catenary.
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