A note on primary-like submodules of multiplication modules

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful property.

Keywords:

Primary , Primary-like submodule , like submodule , weakly primary-like submodule , primeful property , weakly primary , multiplication module