SOME PROPERTIES OF ALMOST JOINTLY PRIME (R,S)-SUBMODULES - Yuwaningsih, Dian Ariesta; Nurnugroho, Burhanudin Arif; Sholiha, Diniar Mar’atus; Lolita, Lolita (Journal of Fundamental Mathematics and Applications (JFMA), 2024)
Let ? and ? be rings with identity. The definition of prime submodule has been generalized to the almost prime submodule. In addition, the definition of prime submodule has also been carried over to the (?,?)-module structure, which is called jointly prime (?,?)-submodules. However, as a generalization of prime submodules, the concept of almost prime submodules has not been carried over to (?,?)-module structures. In this paper, we construct the definition of almost jointly prime (?,?)-submodules as the generalization of jointly prime (?,?)-submodules. We also present several necessary and sufficient conditions for an (?,?)-submodule to be an almost jointly prime (?,?)-submodule.