On 2-absorbing ideals of noncommutative rings. (English) Zbl 1426.16002
Summary: Let \(R\) be a noncommutative ring with identity. We define the notion of a 2-absorbing ideal and show that if the ring is commutative, then the notion is the same as the original definition that of
A. Badawi [Bull. Aust. Math. Soc. 75, No. 3, 417–429 (2007; Zbl 1120.13004)]. We give an example to show that in general these two notions are different. Many properties of 2-absorbing ideals are proved which are similar to the results for commutative rings.
MSC:
| 16D25 | Ideals in associative algebras |
Citations:
Zbl 1120.13004References:
| [1] | A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429. · Zbl 1120.13004 |
| [2] | A. Badawi and Ahmad Yousefian Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math. 39(2) (2013), 441-452. · Zbl 1278.13001 |
| [3] | A. Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submodules, Thai J. Math. 9 (2011), 577-584. · Zbl 1277.13004 |
| [4] | Sh. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7(6) (2012), 265-271. · Zbl 1247.13016 |
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