This study presents new definitions of prime submodules and modules relative to an ideal, highlighting their essential properties.
In this study, we present the concepts of prime submodules relative to an ideal and prime modules relative to an ideal. Let be a unital left -module. A proper submodule of is called prime submodule relative to a proper ideal of , if whenever , then either or . is named a prime module relative to provided (0) is a prime submodule relative to . Many properties of prime submodules (modules) relative to an ideal are given in this paper.
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Ali et al. (2025) studied this question.
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