Topologies on Specg(M)
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 45-53.

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Let R be a G-graded commutative ring with identity and let M be a graded R-module. We endow Specg(M), the collection of all graded prime submodules of M, analogous to that for Spec(R), the spectrum of prime ideals of R, by two topologies: quasi-Zariski topology and Zariski topology. Then we study some properties of these topological spaces.
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Ahmad Yousefian Darani. Topologies on $Spec_g(M)$. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 45-53. https://geodesic-test.mathdoc.fr/item/BASM_2011_3_a3/

[1] Atiyah M. F., Macdonald I. G., Introduction to commutative algebra, Longman Higher Education, New York, 1969 | MR | Zbl

[2] Dauns J., “Prime modules”, J. Reine Angew. Math., 298 (1978), 156–181 | DOI | MR | Zbl

[3] Ebrahimi Atani S., “On graded prime submodules”, Chiang Mai J. Sci., 33:1 (2006), 3–7 | MR

[4] Ebrahimi Atani S., Farzalipour F., “On graded multiplication modules”, Chiang Mai J. Sci. (to appear)

[5] Ebrahimi Atani S., Saraei F. E. K., “Graded modules which satisfy the Gr-Radical formula”, Thai J. Math., 8:1 (2010), 161–170 | MR

[6] Lu C. P., “The Zariski topology on the prime spectrum of a module”, Houston J. Math., 25:3 (1999), 417–425 | MR

[7] McCasland R. L., Moore M. E., Smith P. F., “On the spectrum of a module over a commutative ring”, Comm. Algebra, 25:1 (1997), 79–103 | DOI | MR | Zbl

[8] Oral K. H., Tekir U., Agargun A. G., “On graded prime and primary submodules”, Turk. J. Math., 25:3 (1999), 417–425 | MR

[9] Roberts P. C., Multiplicities and Chern classes in local algebra, Cambridge University Press, 1998 | MR

[10] Sharp R. Y., “Asymptotic behavior of certain sets of attached prime ideals”, J. London Math. Soc. (2), 34 (1986), 212–218 | DOI | MR | Zbl

[11] Yousefian Darani A., Soheilnia F., “2-Absorbing and weakly 2-absorbing submodules”, Thai J. Math. (to appear)