Abstract
References
- D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (5), 1646-1672, 2011.
- D.D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 29 (4), 831-840, 2003.
- S.E. Atani, On graded weakly prime ideals. Turk. J. Math. 30 (4), 351-358, 2006.
- A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75 (3), 417-429, 2007.
- A. Badawi and A.Y. Darani,On weakly 2-absorbing ideals of commutative rings, Hous- ton J. Math. 39 (2), 441-452, 2013.
- N.H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc. 8, 633-637, 1957.
- C. Nastasescu and V.F. Oystaeyen, Graded Ring Theory, Mathematical Library 38, North Holand, Amsterdam, 1983.
- C. Nastasescu and V.F. Oystaeyen, Methods of Graded Rings, LNM 1836, Springer- Verlag, Berlin-Heidelberg, 2004.
- S.H. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Collq. 19, 913-920, 2012.
- S.H. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7 (6), 265- 271, 2012.
- S.H. Payrovi and S. Babaei, On the 2-absorbing ideals in commutative rings, Bull. Malays. Math. Soc. 23, 1511-1526, 2013.
- P.Jr. Quartaro and H.S. Butts, Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52, 91-96, 1975.
- M. Refai and K. Al-Zoubi, On graded primary ideals, Turk. J. Math. 28 (3), 217-229, 2004.
- A. Yousefian-Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submodules, Thai J. Math. 9 (3), 577-584, 2011.
Abstract
In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbing ideals of a graded ring which are different from 2-absorbing and weakly 2-absorbing ideals. We give some properties and characterizations of these ideals and their homogeneous components. We investigate graded (weakly) 2-absorbing ideals of $R_{1}\times R_{2}$ where $R_{1}$ and $R_{2}$ are two graded rings.
Keywords
graded 2-absorbing ideal graded weakly 2-absorbing ideal graded weakly prime ideal graded prime ideal
References
- D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (5), 1646-1672, 2011.
- D.D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 29 (4), 831-840, 2003.
- S.E. Atani, On graded weakly prime ideals. Turk. J. Math. 30 (4), 351-358, 2006.
- A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75 (3), 417-429, 2007.
- A. Badawi and A.Y. Darani,On weakly 2-absorbing ideals of commutative rings, Hous- ton J. Math. 39 (2), 441-452, 2013.
- N.H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc. 8, 633-637, 1957.
- C. Nastasescu and V.F. Oystaeyen, Graded Ring Theory, Mathematical Library 38, North Holand, Amsterdam, 1983.
- C. Nastasescu and V.F. Oystaeyen, Methods of Graded Rings, LNM 1836, Springer- Verlag, Berlin-Heidelberg, 2004.
- S.H. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Collq. 19, 913-920, 2012.
- S.H. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7 (6), 265- 271, 2012.
- S.H. Payrovi and S. Babaei, On the 2-absorbing ideals in commutative rings, Bull. Malays. Math. Soc. 23, 1511-1526, 2013.
- P.Jr. Quartaro and H.S. Butts, Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52, 91-96, 1975.
- M. Refai and K. Al-Zoubi, On graded primary ideals, Turk. J. Math. 28 (3), 217-229, 2004.
- A. Yousefian-Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submodules, Thai J. Math. 9 (3), 577-584, 2011.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 15, 2019 |
| Published in Issue | Year 2019 Volume: 48 Issue: 3 |