On classical 1-absorbing prime submodules

In this study, we aim to introduce the concept of classical 1-absorbing prime submodules of a nonzero unital module M over a commutative ring A with unity. A proper submodule P of M is said to be a classical 1-absorbing prime submodule, if for each m∈ M and nonunits a,b,c∈ A, abcm∈ P implies that abm∈ P or cm∈ P. We give many examples and properties of classical 1-absorbing prime submodules. Also, we investiage the classical 1-absorbing prime submodules of tensor product F⊗ M of a (faithfully) flat A-module F and any A-module M. Furthermore, we determine classical prime, classical 1-absorbing prime and classical 2-absorbing submodules of amalgamated duplication M⋈ I of an A-module M along an ideal I. Also, we characterize local rings (A,𝔪) with 𝔪^2=0 in terms of classical 1-absorbing prime submodules.