Geodesic
On a $C(\Omega)$-algebra of small dimension two and its tensor powers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 35-39

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We build an example of a maximal ideal in the algebra of all continuous functions on a compact whose homological dimension is $1$. It is shown that the small global dimension of this algebra is $2$. We then compute the small global dimensions of its tensor powers. 
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     author = {A. N. Krichevets},
     title = {On a $C(\Omega)$-algebra of small dimension two and its tensor powers},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {35--39},
     publisher = {mathdoc},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a9/}
}
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A. N. Krichevets. On a $C(\Omega)$-algebra of small dimension two and its tensor powers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1982), pp. 35-39. http://geodesic.mathdoc.fr/item/VMUMM_1982_3_a9/