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‎‎n‎‎-copure submodules of modules

Year 2018, Volume: 15 Issue: 2, - , 30.11.2018

Abstract


‎Let $R$ be a commutative ‎ring,‎ $M$ an $R$-module, and ‎n>=1‎‎ an integer‎‎‎‎‎‎‎. ‎In this paper‎, ‎we will introduce the concept of ‎‎n‎-copure submodules of $M$ as a generalization of copure submodules and obtain some related results‎.

References

  • [1] M.M. Ali and D.J. Smith, Pure submodules of multiplication modules, Beiträge Algebra Geom. 45 (1) (2004)61–74.
  • [2] Y. Al-Shaniafi and P. F. Smith, Comultiplication modules over commutative rings, J. Commut. Algebra, 3 (1)(2011), 1-29.
  • [3] W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York-Heidelberg-Berlin,1974.
  • [4] H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007)1189–1201.
  • [5] H. Ansari-Toroghy and F. Farshadifar, Product and dual product of submodules, Far East J. Math. Sci., 25 (3)(2007), 447–455.
  • [6] H. Ansari-Toroghy and F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci. 8 (1) (2009), 105–113.
  • [7] H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc. 38(4) (2012), 987-1005.
  • [8] A. Barnard, Multiplication modules, J. Algebra, 71 (1981), 174–178.
  • [9] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959) 380–398.
  • [10] F. Farshadifar, n-pure submodules, submitted.
  • [11] F. Farshadifar, Copure and 2-absorbing copure submodules, submitted.
  • [12] L. Fuchs, W. Heinzer, and B. Olberding, Commutative ideal theory without finiteness conditions: Irreducibility inthe quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math.249 (2006), 121–145.
  • [13] T. Y. Lam, Lectures on Modules and Rings. Springer 1999.
  • [14] P. Ribenboim, Algebraic Numbers. Wiley 1972.
  • [15] R. Y. Sharp, Step in commutative algebra, Cambridge University Press, 1990.
  • [16] R. Wisbauer, Foundations of Modules and Rings Theory, Gordon and Breach, Philadelphia, PA, 1991.
Year 2018, Volume: 15 Issue: 2, - , 30.11.2018

Abstract

References

  • [1] M.M. Ali and D.J. Smith, Pure submodules of multiplication modules, Beiträge Algebra Geom. 45 (1) (2004)61–74.
  • [2] Y. Al-Shaniafi and P. F. Smith, Comultiplication modules over commutative rings, J. Commut. Algebra, 3 (1)(2011), 1-29.
  • [3] W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York-Heidelberg-Berlin,1974.
  • [4] H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007)1189–1201.
  • [5] H. Ansari-Toroghy and F. Farshadifar, Product and dual product of submodules, Far East J. Math. Sci., 25 (3)(2007), 447–455.
  • [6] H. Ansari-Toroghy and F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci. 8 (1) (2009), 105–113.
  • [7] H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc. 38(4) (2012), 987-1005.
  • [8] A. Barnard, Multiplication modules, J. Algebra, 71 (1981), 174–178.
  • [9] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959) 380–398.
  • [10] F. Farshadifar, n-pure submodules, submitted.
  • [11] F. Farshadifar, Copure and 2-absorbing copure submodules, submitted.
  • [12] L. Fuchs, W. Heinzer, and B. Olberding, Commutative ideal theory without finiteness conditions: Irreducibility inthe quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math.249 (2006), 121–145.
  • [13] T. Y. Lam, Lectures on Modules and Rings. Springer 1999.
  • [14] P. Ribenboim, Algebraic Numbers. Wiley 1972.
  • [15] R. Y. Sharp, Step in commutative algebra, Cambridge University Press, 1990.
  • [16] R. Wisbauer, Foundations of Modules and Rings Theory, Gordon and Breach, Philadelphia, PA, 1991.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Faranak Farshadifar

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 15 Issue: 2

Cite

APA Farshadifar, F. (2018). ‎‎n‎‎-copure submodules of modules. Cankaya University Journal of Science and Engineering, 15(2).
AMA Farshadifar F. ‎‎n‎‎-copure submodules of modules. CUJSE. November 2018;15(2).
Chicago Farshadifar, Faranak. “‎‎n‎‎-Copure Submodules of Modules”. Cankaya University Journal of Science and Engineering 15, no. 2 (November 2018).
EndNote Farshadifar F (November 1, 2018) ‎‎n‎‎-copure submodules of modules. Cankaya University Journal of Science and Engineering 15 2
IEEE F. Farshadifar, “‎‎n‎‎-copure submodules of modules”, CUJSE, vol. 15, no. 2, 2018.
ISNAD Farshadifar, Faranak. “‎‎n‎‎-Copure Submodules of Modules”. Cankaya University Journal of Science and Engineering 15/2 (November 2018).
JAMA Farshadifar F. ‎‎n‎‎-copure submodules of modules. CUJSE. 2018;15.
MLA Farshadifar, Faranak. “‎‎n‎‎-Copure Submodules of Modules”. Cankaya University Journal of Science and Engineering, vol. 15, no. 2, 2018.
Vancouver Farshadifar F. ‎‎n‎‎-copure submodules of modules. CUJSE. 2018;15(2).