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In the present manuscript, we introduce and study the notion of primary submodules as well as P-primary submodules of a module in the intuitionistic L-fuzzy environment. Apart from investigating basic properties of these submodules, we explore some foundational results analogous to corresponding submodules. A suitable characterization of intuitionistic L-fuzzy primary ( P-primary) submodules in terms of primary (P-primary) submodules are presented.

On intuitionistic L-fuzzy primary and P-primary submodules