ON 2-ABSORBING MODULES OVER NONCOMMUTATIVE RINGS

Year 2019, Volume: 25 Issue: 25 , 212 - 223 , 08.01.2019

N. J. Groenewald Bac T. Nguyen

https://doi.org/10.24330/ieja.504155

Cited By: 4

https://izlik.org/JA63BD75GT

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

References

• A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(3) (2007), 417-429.
• A. M. Buhphang and M. B. Rege, Semi-commutative modules and Armendariz modules, Arab J. Math. Sci., 8(1) (2002), 53-65.
• A. Y. Darani and F. Soheilnia, 2-Absorbing and weakly 2-absorbing submodules, Thai J. Math., 9(3) (2011), 577-584.
• J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
• N. J. Groenewald and D. Ssevviiri, Completely prime submodules, Int. Electron. J. Algebra, 13 (2013), 1-14.
• Sh. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Colloq., 19 (2012) 913-920.
• Sh. Payrovi and S. Babaei, On the 2-absorbing submodules, Iran. J. Math. Sci. Inform., 10(1) (2015), 131-137.