The pointfree version of 𝓒_c(X) via the ranges of functions

References

[1] Aliabad, A. R.—Mahmoudi, M.: Pre-image of function in C_c(L), Categ. Gen. Algebr. Struct. Appl. 15(1) (2021), 35–58.Suche in Google Scholar

[2] Atiyah, M. F.—MacDonald, I. G.: Introduction to Commutative Algebra, Addison Wesley Publishing Co., 1969.Suche in Google Scholar

[3] Ball, R. N.—Hager, A. W.: On the localic yosida representation of an archimedean lattice ordered group with weak order unit, J. Pure Appl. Algebra 70 (1991), 17–43.Suche in Google Scholar

[4] Banaschewski, B.: The Real Numbers in Pointfree Topology, Textos de Matemática (Series B), Univ. Coimbra, vol. 12, 1997.Suche in Google Scholar

[5] Dowker, C. H.—Papert, D.: On Urysohn’s lemma, General Topology and its Relations to Modern Analysis, Proceedings of the second Prague topological symposium, 1966. Academia Publishing House of the Czechoslovak Academy of Sciences, 1967, pp. 111–114.Suche in Google Scholar

[6] Dube, T.: Concerning F-frames, Algebra Universalis 62 (2009), 273–288.Suche in Google Scholar

[7] Dube, T.: Concerning P-frames, essential P-frames, and strongly zero-dimensional frames, Algebra Universalis 61 (2009), 115–138.Suche in Google Scholar

[8] Dube, T.: Some ring-theoretic properties of almost P-frames, Algebra Universalis. 60 (2009), 145–162.Suche in Google Scholar

[9] Dube, T.: More ring-theoteric characterization of P-frames, J. Algebra Appl. 14(5) (2015), Art. ID 1550061.Suche in Google Scholar

[10] Dube, T.—Ighedo, O.: On z-ideals of pointfree function rings, Bull. Iranian Math. Soc. 40(3) (2014), 657–675.Suche in Google Scholar

[11] Estaji, A. A.—Karimi Feizabadi, A.—Abedi, M.: Zero set in pointfree topology and strongly z-ideals, Bull. Iranian Math. Soc. 41(5) (2015), 1071–1084.Suche in Google Scholar

[12] Estaji, A. A.—Karimi Feizabadi, A.—Robat Sarpoushi, M.: z_c-ideals and prime ideals in ring 𝓡_c(L), Filomat 32 (2018), 6741–6752.Suche in Google Scholar

[13] Estaji, A. A.—Robat Sarpoushi, M.: Locally functionally countable subalgebra of 𝓡(L), Arch. Math. (Brno) 56 (2020), 127–140.Suche in Google Scholar

[14] Estaji, A. A.—Robat Sarpoushi, M.—Elyasi, M.: Further thoughts on the ring 𝓡_c(L) in frames, Algebra Universalis 80 (2019), Art. No. 43.Suche in Google Scholar

[15] Estaji, A. A.—Taha, M.: The clean elements of the ring 𝓡(L) and 𝓒_c(L), Algebra Universalis 80(4) (2019), 1–14.Suche in Google Scholar

[16] Estaji, A. A.—Taha, M.: Cozero part of the pointfree vertion of 𝓒_c(L), Czechoslovak Math. J., accepted.Suche in Google Scholar

[17] Ghadermazi, M.—Karamzadeh, O. A. S.—Namdari, M.: On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69.Suche in Google Scholar

[18] Gillman, L.—Jerison, M.: Rings of Continuous Functions, Springer-Verlag, 1976.Suche in Google Scholar

[19] Henriksen, M.—Jerison, M.: The space of minimal prime ideals of a commutative ring, Trans. Amer. Math. Soc. 115 (1965), 110–130.Suche in Google Scholar

[20] Johnstone, P. T.: Stone Spaces, Cambridge Univ. Press, Cambridge, 1982.Suche in Google Scholar

[21] Karamzadeh, O. A. S.—Rostami, M.: On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93(1) (1985), 179–184.Suche in Google Scholar

[22] Karamzadeh, O. A. S.—Namdari, M.—Soltanpour, S.: On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol. 16 (2015), 183–207.Suche in Google Scholar

[23] Karimi Feizabadi, A.—Estaji, A. A.—Robat Sarpoushi, M.: Pointfree version of image of real-valued continuous functions, Categ. Gen. Algebr. Struct. Appl. 9(1) (2018), 59–75.Suche in Google Scholar

[24] Mehri, R.—Mohamadian, R.: On the locally countable subalgebra of C(X) whose local domain is cocountable, Hacet. J. Math. Stat. 46(6) (2017), 1053–1068.Suche in Google Scholar

[25] Namdari, M.—Veisi, A.: Rings of quotients of the subalgebra of C(X) consisting of functions with countable image, Inter. Math. Forum 7 (2012), 561–571.Suche in Google Scholar

[26] Sharp, R. Y.: Steps in Commutative Algebra, Cambridge Univ. Press, 2000.Suche in Google Scholar

[27] Taha, M.—Estaji, A. A.—Robat Sarpoushi, M.: On the regularity of 𝓒_c(L), 53-nd Annual Iranian Mathematics Conference University of Science, September 5-8, Technology of Mazandaran, 2022.Suche in Google Scholar