Research Article
BibTex RIS Cite

On Coatomic Semimodules over Commutative Semirings

Year 2011, Volume: 8 Issue: 2, - , 01.11.2011

S. Ebrahimi Atani F. Esmaeili Khalil Saraei

Abstract

This paper generalizes some well known results on coatomic and semisimple
modules in commutative rings to coatomic and semisimple semimodules over commutative
semirings. The main difficulty is figuring out what additional hypotheses the subsemimodules
must satisfy to get similar results. It is proved that k-subsemimodules of semimodules
are important in the study of semimodules.

Keywords

Semiring coatomic semimodules semisimple semimodules k-supplemented semimodules

References

  • [1] G. Bilhan and T. Guroglu, W-Coatomic modules, Cankaya University Journal of Science and Engineering 7 (2010), 17-24.
  • [2] J. N. Chaudhari and D. R. Bonde, On partitioning and subtractive subsemimodules of semimodules over semirings, Kyungpook Mathematical Journal 50 (2010), 329-336.
  • [3] R. E. Atani and S. E. Atani, Ideal theory in commutative semirings, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica 2 (2008), 14-23.
  • [4] R. E. Atani and S. E. Atani, On subsemimodules of semimodules, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica 2 (2010), 20-30.
  • [5] S. E. Atani and R. E. Atani, Some remarks on partitioning semirings, Analele Stiinti ce ale Universitatii Ovidius Constanta Seria Matematica 18 (2010), 49-62.
  • [6] J. S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999.
  • [7] J. S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science (Pitman Monographs and Surveys in Pure and Applied Mathematics), Longman Scienti c and Thechnical, Harlow UK 1992.
  • [8] G. Gungoroglu, Coatomic modules, Far East Journal of Mathematical Sciences Special Volume, Part II (1998), 153-162.
  • [9] U. Hebisch and H. J. Weinert, Halbringe Algebraische Theorie und Anwendungen in der Informatik, Teubner Studienbucher, Stuttgart 1993.
  • [10] N. X. Tuyen and H. X. Thang, On superuous subsemimodules, Georgian Mathematical Journal 10 (2003), 763-770.
  • [11] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia 1991.
  • [12] H. Zoschinger, Koatomare Moduln, Mathematische Zeitschrift 170 (1980), 221-232.

Year 2011, Volume: 8 Issue: 2, - , 01.11.2011

S. Ebrahimi Atani F. Esmaeili Khalil Saraei

Abstract

References

  • [1] G. Bilhan and T. Guroglu, W-Coatomic modules, Cankaya University Journal of Science and Engineering 7 (2010), 17-24.
  • [2] J. N. Chaudhari and D. R. Bonde, On partitioning and subtractive subsemimodules of semimodules over semirings, Kyungpook Mathematical Journal 50 (2010), 329-336.
  • [3] R. E. Atani and S. E. Atani, Ideal theory in commutative semirings, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica 2 (2008), 14-23.
  • [4] R. E. Atani and S. E. Atani, On subsemimodules of semimodules, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica 2 (2010), 20-30.
  • [5] S. E. Atani and R. E. Atani, Some remarks on partitioning semirings, Analele Stiinti ce ale Universitatii Ovidius Constanta Seria Matematica 18 (2010), 49-62.
  • [6] J. S. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht 1999.
  • [7] J. S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science (Pitman Monographs and Surveys in Pure and Applied Mathematics), Longman Scienti c and Thechnical, Harlow UK 1992.
  • [8] G. Gungoroglu, Coatomic modules, Far East Journal of Mathematical Sciences Special Volume, Part II (1998), 153-162.
  • [9] U. Hebisch and H. J. Weinert, Halbringe Algebraische Theorie und Anwendungen in der Informatik, Teubner Studienbucher, Stuttgart 1993.
  • [10] N. X. Tuyen and H. X. Thang, On superuous subsemimodules, Georgian Mathematical Journal 10 (2003), 763-770.
  • [11] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia 1991.
  • [12] H. Zoschinger, Koatomare Moduln, Mathematische Zeitschrift 170 (1980), 221-232.
There are 12 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

S. Ebrahimi Atani This is me

F. Esmaeili Khalil Saraei This is me

Publication Date November 1, 2011
Published in Issue Year 2011 Volume: 8 Issue: 2

Cite

APA Atani, S. E., & Saraei, F. E. K. (2011). On Coatomic Semimodules over Commutative Semirings. Cankaya University Journal of Science and Engineering, 8(2).
AMA Atani SE, Saraei FEK. On Coatomic Semimodules over Commutative Semirings. CUJSE. November 2011;8(2).
Chicago Atani, S. Ebrahimi, and F. Esmaeili Khalil Saraei. “On Coatomic Semimodules over Commutative Semirings”. Cankaya University Journal of Science and Engineering 8, no. 2 (November 2011).
EndNote Atani SE, Saraei FEK (November 1, 2011) On Coatomic Semimodules over Commutative Semirings. Cankaya University Journal of Science and Engineering 8 2
IEEE S. E. Atani and F. E. K. Saraei, “On Coatomic Semimodules over Commutative Semirings”, CUJSE, vol. 8, no. 2, 2011.
ISNAD Atani, S. Ebrahimi - Saraei, F. Esmaeili Khalil. “On Coatomic Semimodules over Commutative Semirings”. Cankaya University Journal of Science and Engineering 8/2 (November 2011).
JAMA Atani SE, Saraei FEK. On Coatomic Semimodules over Commutative Semirings. CUJSE. 2011;8.
MLA Atani, S. Ebrahimi and F. Esmaeili Khalil Saraei. “On Coatomic Semimodules over Commutative Semirings”. Cankaya University Journal of Science and Engineering, vol. 8, no. 2, 2011.
Vancouver Atani SE, Saraei FEK. On Coatomic Semimodules over Commutative Semirings. CUJSE. 2011;8(2).