Research Article
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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.

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

Bibtex @research article { ieja296034, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2017}, volume = {21}, number = {21}, pages = {76 - 90}, doi = {10.24330/ieja.296034}, title = {ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS}, key = {cite}, author = {Atani, S. Ebrahimi and Bazari, M. Sedghi Shanbeh} }
APA Atani, S. E. & Bazari, M. S. S. (2017). ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS . International Electronic Journal of Algebra , 21 (21) , 76-90 . DOI: 10.24330/ieja.296034
MLA Atani, S. E. , Bazari, M. S. S. "ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS" . International Electronic Journal of Algebra 21 (2017 ): 76-90 <https://dergipark.org.tr/en/pub/ieja/issue/27921/296034>
Chicago Atani, S. E. , Bazari, M. S. S. "ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS". International Electronic Journal of Algebra 21 (2017 ): 76-90
RIS TY - JOUR T1 - ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS AU - S. EbrahimiAtani, M. Sedghi ShanbehBazari Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296034 DO - 10.24330/ieja.296034 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 76 EP - 90 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296034 UR - https://doi.org/10.24330/ieja.296034 Y2 - 2016 ER -
EndNote %0 International Electronic Journal of Algebra ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS %A S. Ebrahimi Atani , M. Sedghi Shanbeh Bazari %T ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296034 %U 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
AMA Atani S. E. , Bazari M. S. S. ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. 2017; 21(21): 76-90.
Vancouver Atani S. E. , Bazari M. S. S. ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS. International Electronic Journal of Algebra. 2017; 21(21): 76-90.
IEEE S. E. Atani and M. S. S. Bazari , "ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS", International Electronic Journal of Algebra, vol. 21, no. 21, pp. 76-90, Jan. 2017, doi:10.24330/ieja.296034