On graded 2-absorbing and graded weakly2-absorbing ideals

On graded 2-absorbing and graded weakly2-absorbing ideals

In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbingideals 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 homogeneouscomponents. We investigate graded (weakly) 2-absorbing ideals of$R_1$×$R_2$where$R_1$and$R_2$are two graded rings.

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  • [1]D.F. Anderson and A. Badawi,On n-absorbing ideals of commutative rings, Comm.Algebra39(5), 1646-1672, 2011.
  • [2]D.D. Anderson and E. Smith,Weakly prime ideals, Houston J. Math.29(4), 831-840,2003.
  • [3]S.E. Atani,On graded weakly prime ideals. Turk. J. Math.30(4), 351-358, 2006.
  • [4]A. Badawi,On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc.75(3), 417-429, 2007.
  • [5]A. Badawi and A.Y. Darani,On weakly 2-absorbing ideals of commutative rings, Hous-ton J. Math.39(2), 441-452, 2013.
  • [6]N.H. McCoy,A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc.8, 633-637, 1957.
  • [7]C. Nastasescu and V.F. Oystaeyen,Graded Ring Theory, Mathematical Library 38,North Holand, Amsterdam, 1983.
  • [8]C. Nastasescu and V.F. Oystaeyen,Methods of Graded Rings, LNM 1836, Springer-Verlag, Berlin-Heidelberg, 2004.
  • [9]S.H. Payrovi and S. Babaei,On 2-absorbing submodules, Algebra Collq.19, 913-920,2012.
  • [10]S.H. Payrovi and S. Babaei,On the 2-absorbing ideals, Int. Math. Forum7(6), 265-271, 2012.
  • [11]S.H. Payrovi and S. Babaei,On the 2-absorbing ideals in commutative rings, Bull.Malays. Math. Soc.23, 1511-1526, 2013.
  • [12]P.Jr. Quartaro and H.S. Butts,Finite unions of ideals and modules, Proc. Amer.Math. Soc.52, 91-96, 1975.
  • [13]M. Refai and K. Al-Zoubi,On graded primary ideals, Turk. J. Math.28(3), 217-229,2004.
  • [14]A. Yousefian-Darani and F. Soheilnia,2-absorbing and weakly 2-absorbing submodules,Thai J. Math.9(3), 577-584, 2011.