Contracting the socle in rings of continuous functions

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1. [1] R. N. Ball - J. Walters-Wayland, $C$- and $C^{*}$-quotients in pointfree topology, Dissertationes Mathematicae (Rozprawy Mat.), Vol. 412 (2002), p. 62. Zbl1012.54025MR1952051
2. [2] B. Banaschewski, The real numbers in pointfree topology, Textos de Matemática Série B, No. 12, Departamento de Matemática da Universidade de Coimbra, 1997. Zbl0891.54009MR1621835
3. [3] B. Banaschewski, Gelfand and exchange rings: Their spectra in pointfree topology, The Arabian J. Science and Engineering, 25 (2000), pp. 3--22. Zbl1271.13052MR1829217
4. [4] B. Banaschewski, On the function ring functor in pointfree topology, Appl. Categor. Struct., 13 (2005), pp. 305--328. Zbl1158.54308MR2175953
5. [5] B. Banaschewski - C. Gilmour, Pseudocompactness and the cozero part of a frame, Comment. Math. Univ. Carolinae, 37(3) (1996), pp. 577--587. Zbl0881.54018MR1426922
6. [6] T. Dube, Some ring-theoretic properties of almost $P$-frames, Alg. Univ., 60 (2009), pp. 145--162. Zbl1186.06006MR2491419
7. [7] T. Dube, Notes on pointfree disconnectivity with a ring-theoretic slant, Appl. Categor. Struct., 18 (2010), pp. 55--72. Zbl1188.06005MR2586718
8. [8] T. Dube, Concerning $P$-, essential $P$- and strongly zero-dimensional frames, Alg. Univ., 69 (2009), pp. 115--138. Zbl1190.06007MR2551788
9. [9] M. W. Evans, Exoteric homomorphisms, J. Pure Appl. Alg., 49 (1987), pp. 117--131. Zbl0636.13003MR920517
10. [10] L. Gillman - M. Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, 1960. Zbl0093.30001MR116199
11. [11] M. Henriksen - M. Jerison, The space of minimal prime ideals of a commutative ring, Trans. Amer. Math. Soc., 115 (1965), pp. 110--130. Zbl0147.29105MR194880
12. [12] J. Lambek, Lecture notes on rings and modules, Chelsea Publ. Co. (New York, 1976). Zbl0365.16001
13. [13] P. T. Johnstone, Stone Spaces, Cambridge Univ. Press (Cambridge, 1982). Zbl0586.54001MR698074
14. [14] O. A. S. Karamzadeh - M. Rostami, On the intrisic topology and some related ideals of $C\left(X\right)$, Proc. Amer. Math. Soc., 93 (1) (1985), pp. 179--184. Zbl0524.54013MR766552
15. [15] R. G. Woods, Maps that characterize normality properties and pseudocompactness, J. London Math. Soc., 7 (2) (1973), pp. 453--461. Zbl0271.54005MR346731

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