Geodesic
Projective ideals of Banach algebras and approximative units
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1119-1123

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It is shown that if an ideal of a commutative Banach algebra has a Schauder base, then it is projective iff it contains an approximative unit with some special properties. For uniform algebras a criterion is formulated in terms of peak sets. 
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     author = {L. I. Pugach},
     title = {Projective ideals of {Banach} algebras and approximative units},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1119--1123},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a23/}
}
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L. I. Pugach. Projective ideals of Banach algebras and approximative units. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1119-1123. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a23/