On graded primary-like submodules of graded modules over graded commutative rings

• Al-Zoubi, Khaldoun ^[1] ; Al-Dolat, Mohammed ^[1]
  1. [1] Jordan University of Science and Technology

     Jordan University of Science and Technology

     Jordania

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 4, 2021, págs. 859-871
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-3467
• Enlaces
  • Texto completo
• Resumen

  • Let G be a group with identity e. Let R be a G-graded commutative ring andM a graded R-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give some basic results about graded primary-like submodules of graded modules. Special attention has been paid, when graded submodules satisfies the gr-primeful property, to and extra properties of these graded submodules.

• Referencias bibliográficas
  • K. Al-Zoubi, “The graded primary radical of a graded submodules”, Analele ştiinţifice ale Universităţii "Al.I. Cuza" din Iaşi. Matematică...
  • K. Al-Zoubi and R. Abu-Dawwas, “On graded quasi-prime submodules”, Kyungpook mathematical journal, vol. 55, no. 2, pp. 259-266, 2015. http://dx.doi.org/10.5666/KMJ.2015.55.2.259
  • K. Al-Zoubi, R. Abu-Dawwas and I. Al-Ayyoub, “Graded semiprime submodules and graded semi-radical of graded submodules in graded modules”,...
  • 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,...
  • K. Al-Zoubi, M. Jaradat and R. Abu-Dawwas, “On graded classical prime and graded prime submodules”, Bulletin of the Iranian Mathematical Society,...
  • K. Al-Zoubi and F. Qarqaz, “An intersection condition for graded prime submodules in Gr-multiplication modules”, Mathematicals reports, vol....
  • S. E. Atani, “On graded prime submodules”, Chiang mai journal of science, vol. 33, no. 1, pp. 3-7, 2006. [On line]. Available: https://bit.ly/3wmHTYr
  • S. E. Atani and R. E. Atani, “Graded multiplication modules and the graded ideal θg(M)”, Turkish journal of mathematics, vol. 35, no. 1, pp....
  • S. E. Atani and F. Farzalipour, “Notes on the graded prime submodules”, International mathematical forum, vol. 1, no. 38, pp. 1871-1880, 2006....
  • S. E. Atani and F. E. K. Saraei, “Graded modules which satisfy the Gr-radical formula”, Thai journal of mathematics , vol. 8, no. 1, pp. 161-170,...
  • S. E. Atani and F. Farzalipour, “On graded secondary modules”, Turkish journal of mathematics, vol. 31, no. 4, pp. 371-378, 2007. [On line]....
  • J. Escoriza and B. Torrecillas, “Multiplication objects in commutative Grothendieck categories”, Communications in algebra, vol. 26, no. 6,...
  • P. Ghiasvand and F. Farzalipour, “On graded primary submodules of graded multiplication modules”, International journal of algebra, vol. 4,...
  • R. Hazrat, Graded rings and graded Grothendieck groups, Cambridge: Cambridge University Press, 2016. https://doi.org/10.1017/CBO9781316717134
  • C. P. Lu, “A module whose prime spectrum has the surjective natural map”, Houston journal of mathematics, vol. 33, no. 1, pp. 125-143, 2007....
  • S.C. Lee and R. Varmazyar, “Semiprime submodules of graded multiplication modules”, Journal of the Korean Mathematical Society, vol. 49, no....
  • H. F. Moghimi and F. Rashedi, “Primary-like submodules satisfying the primeful property”, Transactions on Algebra and its Applications, vol....
  • C. Nastasescu and .F. Oystaeyen, Graded and filtered rings and modules. Berlin: Springer, 1979. https://doi.org/10.1007/BFb0067331
  • C. Nastasescu, F. Oystaeyen, Graded ring theory, Amsterdam: North Holland, 1982.
  • C. Nastasescu and F. Oystaeyen, Methods of graded rings. Berlin: Springer, 2004. https://doi.org/10.1007/b94904
  • K. H. Oral, U. Tekir and A.G. Agargun, “On Graded prime and primary submodules”, Turkish journal of mathematics, vol. 35, no. 2, pp. 159-167,...
  • M. Refai and K. Al-Zoubi, “On graded primary ideals”, Turkish journal of mathematics, vol. 28, no. 3, pp. 217-229, 2004. [On line]. Available:...
  • M. Refai, M. Hailat and S. Obiedat, “Graded radicals on graded prime spectra”, Far East journal of mathematical sciences, vol. 1, no. 1, pp....
  • H. A. Tavallaee and M. Zolfaghari, “Graded weakly semiprime submodules of graded multiplication modules”, Lobachevskii journal of mathematics,...