ON 2-ABSORBING MODULES OVER NONCOMMUTATIVE RINGS

Abstract

Let R be a noncommutative ring with identity. We dene the

notion of a 2-absorbing submodule and show that if the ring is commutative

then the notion is the same as the original denition of that of A. Darani and

F. Soheilnia. We give an example to show that in general these two notions

are dierent. Many properties of 2-absorbing submodules are proved which

are similar to the results for commutative rings.

Keywords

• 2-Absorbing submodule,strong 2-absorbing submodule,prime submodule,completely prime submodule

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