H. Fazaeli Moghimi - University of Birjand
F. Rashedi - University of Birjand
M. Samiei - University of Birjand

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.

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