SciELO - Scientific Electronic Library Online

 
vol.38 número4Nonlinear elliptic problems in weighted variable exponent Sobolev spaces by topological degreeSome fixed point theorems for generalized Kannan type mappings in b-metric spaces índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0049 

Articles

On graded 2-classical prime submodules of graded modules over graded commutative rings

Khaldoun Al-Zoubi1 
http://orcid.org/0000-0001-6082-4480

Farah Al-Turman2 

1Jordan University of Science and Technology, Dept.of Mathematics and Statistics, Irbid, Jordan, e-mail: kfzoubi@just.edu.jo

2Jordan University of Science and Technology, Dept.of Mathematics and Statistics, Irbid, Jordan fgalturman15@sci.just.edu.jo

Abstract

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-classical prime submodules. Various properties of graded 2-classical prime submodules are considered.

Keywords: Graded 2-classical prime submodule; Graded classical prime submodule; Graded prime submodule

Texto completo disponible sólo en PDF.

Full text . Available only in PDF format.

Acknowledgements

The authors wish to thank sincerely the referees for their valuable comments

and suggestions.

References

[1] K. Al-Zoubi and R. Abu-Dawwas , “On graded 2-absorbing and weakly graded 2-absorbing submodules”, Journal of mathematical sciences: advances and applications, vol. 28, pp. 45- 60, 2014. [On line]. Available: https://bit.ly/2Jk4xuTLinks ]

[2] K. Al-Zoubiand R. Abu-Dawwas , “On graded quasi-prime submodules”, Kyungpook mathematical journal, vol. 55, no. 2, pp. 259-266, Jun. 2015. [On line]. Available: https://bit.ly/2MUtm19Links ]

[3] K. Al-Zoubi , M. Jaradat and R. Abu-Dawwas , “On graded classical prime and graded prime submodules”, Bulletin of the iranian mathematical society, vol. 41, no. 1, pp. 217-225, 2015. [On line]. Available: https://bit.ly/2MteIz8Links ]

[4] K. Al-Zoubi and M. Al-Dolat , “On graded classical primary submodules”, Advances in pure and applied mathematics, vol. 7, no. 2, pp. 93-96, 2016, doi: 10.1515/apam-2015-0021. [ Links ]

[5] K. Al-Zoubi and F. Qarqaz, “An intersection condition for graded prime submodules”, Mathematical reports, vol. 20, no. 3, pp. 329-336, 2018. [On line]. Available: https://bit.ly/2P27ELBLinks ]

[6] S. Atani, “On graded prime submodules”, Chiang Mai journal of science, vol. 33, no. 1, pp. 3-7, 2006. [On line]. Available: https://bit.ly/2o0Ab9bLinks ]

[7] S. Atani, “On graded weakly prime ideals”, Turkish journal of mathematics, vol. 30, no. 4, pp. 351-358, 2006. [On line]. Available: https://bit.ly/2BtfiqmLinks ]

[8] S. Atani and F. Farzalipour, On graded secondary modules, Turkish journal of mathematics , vol. 31, no. 4, pp. 371-378, 2007. [On line]. Available: https://bit.ly/2J3xgE3Links ]

[9] P. Deligne, P. Etingof, D. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D. Morrison and E. Witten, Eds., Quantum fields and strings: a course for mathematicians. Providence, RI: American Mathematical Society, 1999. [ Links ]

[10] A. Darani and S. Motmaen,” Zariski topology on the spectrum of graded classical prime submodules”, Applied general topology, vol. 14, no. 2, pp. 159-169, 2013, doi: 10.4995/agt.2013.1586. [ Links ]

[11] I. Kolar, P. Michor, and J. Slovak, Natural operations in differential geometry, Berlin: Springer, 2010, doi: 10.1007/978-3-662-02950-3. [ Links ]

[12] R. Hazrat, Graded rings and graded grothendieck groups, vol. 435. Cambridge: Cambridge University Press, 2016, doi: 10.1017/CBO9781316717134. [ Links ]

[13] C. Năstăsescu and F. Van Oystaeyen, Graded and filtered rings and modules, vol. 758. Berlin: Springer , 1979, doi: 10.1007/BFb0067331. [ Links ]

[14] C. Năstăsescu and F. Van Oystaeyen, Graded ring theory, vol. 28. Amsterdam: Elsevier, 1982. [On line]. Available: https://bit.ly/2BrtNLmLinks ]

[15] C. Năstăsescu and F. Van Oystaeyen, Methods of graded rings, vol. 1836. Berlin: Springer , 2004, doi: 10.1007/b94904. [ Links ]

[16] K. Oral, U. Tekir and A. Agargun, “On graded prime and primary submodules”, Turkish journal of mathematics , vol. 35, no. 2, pp. 159-167, 2011. [On line]. Available: https://bit.ly/2VUgdJALinks ]

[17] A. Rogers, Supermanifolds: theory and applications. Singapore: World Scientific, 2007, doi:10.1142/1878 . [ Links ]

[18] M. Refai andK. Al-Zoubi , “On graded primary ideals”, Turkish journal of mathematics , vol. 28, no. 3, pp. 217-229, 2004. [On line]. Available: https://bit.ly/2VYd63fLinks ]

[19] M. Refai , M. Hailat and S. Obiedat, “Graded radicals on graded prime spectra”, Far East journal of mathematical sciences, vol. 1, pp. 59-73, 2000. [ Links ]

[20] R. Uregen, U. Tekir and K. Oral, “On the union of graded prime ideals”, Open physics, vol. 14, no. 1 pp. 114-118, 2016, doi: 10.1515/phys-2016-0011. [ Links ]

Recibido: Julio de 2018; Aprobado: Marzo de 2019

Creative Commons License Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons