Zariski topology on the spectrum of graded classical prime submodules

[EN] 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 ¿ h(R), m ¿ h(M), whenever abm ¿ N, then either am ¿ N or bm ¿ N. The spectrum of graded classical prime submodules of M is denoted by Cl.Specg(M). We topologize Cl.Specg (M) with the quasi-Zariski topology, which is analogous to that for Specg(R).Yousefian Darani, A.; Motmaen, S. (2013). Zariski topology on the spectrum of graded classical prime submodules. Applied General Topology. 14(2):159-169. doi:10.4995/agt.2013.1586.SWORD159169142S. 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.McCasland, R. L., Moore, M. E., & Smith, P. F. (1997). On the spectrum of a module over a commutative ring. Communications in Algebra, 25(1), 79-103. doi:10.1080/00927879708825840K. H. Oral, U. Tekir and A.G. Agargun, On graded prime and primary submodules, Turk. J. Math. 25, no. 3 (1999), 417-425.Roberts, P. C. (1998). Multiplicities and Chern Classes in Local Algebra. doi:10.1017/cbo9780511529986Sharp, R. Y. (1986). Asymptotic Behaviour of Certain Sets of Attached Prime Ideals. Journal of the London Mathematical Society, s2-34(2), 212-218. doi:10.1112/jlms/s2-34.2.212BAZIAR, M., & BEHBOODI, M. (2009). CLASSICAL PRIMARY SUBMODULES AND DECOMPOSITION THEORY OF MODULES. Journal of Algebra and Its Applications, 08(03), 351-362. doi:10.1142/s0219498809003369M. 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), 255–271.M. Behboodi and S. H. Shojaee, On chains of classical prime submodules and dimension theory of modules, Bulletin of the Iranian Mathematical Society 36 (2010), 149–166.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