Geodesic
Homological properties of algebra $C(X)$ in non-Archimedean analysis
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1037-1046

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In this article the author offers a variant of homological theory in non-Archimedean analysis and computes the left global dimension and bidimension of an algebra $C(X)$ of all continuous functions on an ultrametrizable compact set $X$. To the moment the analogous problem in Archimedean analysis is still not solved. More generally, the author computes the homological dimensions of ideals $I\subset C(X)$ as left modules and bimodules. 
@article{FPM_2001_7_4_a4,
     author = {A. V. Kuzmin},
     title = {Homological properties of algebra $C(X)$ in {non-Archimedean} analysis},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1037--1046},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a4/}
}
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A. V. Kuzmin. Homological properties of algebra $C(X)$ in non-Archimedean analysis. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 4, pp. 1037-1046. http://geodesic.mathdoc.fr/item/FPM_2001_7_4_a4/