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ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS

Year 2017, Volume: 21 Issue: 21, 76 - 90, 17.01.2017
https://doi.org/10.24330/ieja.296034

Abstract

Following some ideas and a technique introduced in [Comm. Algebra
41 (2013), pp. 776-791] we give a complete classification, up to isomorphism,
of all indecomposable 2-absorbing multiplication modules with finitedimensional
top over pullback of two discrete valuation domains with the same
residue field.

References

  • [1] D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pullback
  • rings, J. Algebra, 184(1) (1996), 304-332.
  • [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math.
  • Soc., 75(3) (2007), 417-429.
  • [3] A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative
  • rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
  • [4] A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of
  • commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
  • [6] Ju. A. Drozd, Matrix problems and categories of matrices, In: Zap. Nauchn.
  • Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 28 (1972), 144-153 (in
  • Russian).
  • [7] S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra,
  • 28(9) (2000), 4037-4069.
  • [8] S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast
  • Asian Bull. Math, 25(1) (2001), 1-6.
  • [9] S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra,
  • 30(6) (2002), 2675-2685.
Year 2017, Volume: 21 Issue: 21, 76 - 90, 17.01.2017
https://doi.org/10.24330/ieja.296034

Abstract

References

  • [1] D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pullback
  • rings, J. Algebra, 184(1) (1996), 304-332.
  • [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math.
  • Soc., 75(3) (2007), 417-429.
  • [3] A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative
  • rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
  • [4] A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of
  • commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
  • [6] Ju. A. Drozd, Matrix problems and categories of matrices, In: Zap. Nauchn.
  • Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 28 (1972), 144-153 (in
  • Russian).
  • [7] S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra,
  • 28(9) (2000), 4037-4069.
  • [8] S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast
  • Asian Bull. Math, 25(1) (2001), 1-6.
  • [9] S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra,
  • 30(6) (2002), 2675-2685.
There are 17 citations in total.

Details

Journal Section Articles
Authors

S. Ebrahimi Atani

M. Sedghi Shanbeh Bazari

Publication Date January 17, 2017
Published in Issue Year 2017 Volume: 21 Issue: 21

Cite

APA Atani, S. E., & Bazari, M. S. S. (2017). ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. International Electronic Journal of Algebra, 21(21), 76-90. https://doi.org/10.24330/ieja.296034
AMA Atani SE, Bazari MSS. ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. January 2017;21(21):76-90. doi:10.24330/ieja.296034
Chicago Atani, S. Ebrahimi, and M. Sedghi Shanbeh Bazari. “ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra 21, no. 21 (January 2017): 76-90. https://doi.org/10.24330/ieja.296034.
EndNote Atani SE, Bazari MSS (January 1, 2017) ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. International Electronic Journal of Algebra 21 21 76–90.
IEEE S. E. Atani and M. S. S. Bazari, “ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS”, IEJA, vol. 21, no. 21, pp. 76–90, 2017, doi: 10.24330/ieja.296034.
ISNAD Atani, S. Ebrahimi - Bazari, M. Sedghi Shanbeh. “ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra 21/21 (January 2017), 76-90. https://doi.org/10.24330/ieja.296034.
JAMA Atani SE, Bazari MSS. ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. 2017;21:76–90.
MLA Atani, S. Ebrahimi and M. Sedghi Shanbeh Bazari. “ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra, vol. 21, no. 21, 2017, pp. 76-90, doi:10.24330/ieja.296034.
Vancouver Atani SE, Bazari MSS. ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. 2017;21(21):76-90.