Zariski topology on the spectrum of graded classical prime submodules

• Yousefian Darani, Ahmad ^[1] ; Motmaen, Shahram ^[2]
  1. [1] University of Mohaghegh Ardabili

     University of Mohaghegh Ardabili

     Irán

     
  2. [2] Islamic Azad University

     Islamic Azad University

     Irán

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 14, Nº. 2, 2013, págs. 159-169
• Idioma: inglés
• DOI: 10.4995/agt.2013.1586
• Enlaces
  • Texto completo
• Resumen

  • Let $R$ be a $G$-graded commutative ring with identity and let $M$ be a graded $R$-module. A proper graded submodule $N$ of $M$ is called graded classical prime if for every $a, b\in h(R)$, $m\in h(M)$, whenever $abm\in N$, then either $am\in N$ or $bm\in N$. The spectrum of graded classical prime submodules of $M$ is denoted by $Cl.Spec_g(M)$. We topologize $Cl.Spec_g(M)$ with the quasi-Zariski topology, which is analogous to that for $Spec_g(R)$.

• Referencias bibliográficas
  • S. Ebrahimi Atani and F. Farzalipour, On weakly prime submodules, Tamkang Journal of Mathematics 38, no. 3 (2007), 247-252.
  • S. Ebrahimi Atani and F. Farzalipour, On graded multiplication modules, Chiang-Mai Journal of Science, to appear.
  • S. Ebrahimi Atani and F.E.K. Saraei, Graded modules which satisfy the Gr-Radical formola, Thai Journal of Mathematics 8, no. 1 (2010), 161-170.
  • P. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math. 25, no. 3 (1999), 417-425.
  • R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra 25, no. 1 (1997), 79-103....
  • K. H. Oral, U. Tekir and A.G. Agargun, On graded prime and primary submodules, Turk. J. Math. 25, no. 3 (1999), 417-425.
  • P. C. Roberts, Multiplicities and Chern classes in local algebra, Cambridge University Press, 1998. http://dx.doi.org/10.1017/CBO9780511529986
  • R. Y. Sharp, Asymptotic behaviour of certain sets of attached prime ideals, J. London Math. Soc. 34, no. 2 (1986), 212-218. http://dx.doi.org/10.1112/jlms/s2-34.2.212
  • Yousefia Darani, Topologies on $Spec_g(M)$, Buletinul Academiei de Stiinte a Republicii Moldova Matematica, to appear.
  • M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Longman Higher Education, New York 1969.
  • M. Baziar and M. Behboodi, Classical primary submodules and decomposition theory of modules, J. Algebra Appl. 8, no. 3 (2009), 351–362. http://dx.doi.org/10.1142/S0219498809003369
  • M. Behboodi and H. Koohi, Weakly prime modules, Vietnam J. Math. 32, no. 2 (2004), 185–195.
  • M. Behboodi and M. J. Noori, Zariski-Like topology on the classical prime spectrum of a module, Bull. Iranian Math. Soc. 35, no. 1 (2009),...
  • M. Behboodi and S. H. Shojaee, On chains of classical prime submodules and dimension theory of modules, Bulletin of the Iranian Mathematical...
  • J. Dauns, Prime modules, J. Reine Angew. Math. 298 (1978), 156–181.
  • S. Ebrahimi Atani, On graded prime submodules, Chiang Mai J. Sci. 33, no. 1 (2006), 3–7.