Geodesic
Annihilators in infinite-dimensional Grassmann–Banach algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 30-40 
V. D. Ivashchuk. Annihilators in infinite-dimensional Grassmann–Banach algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 1, pp. 30-40. http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a2/
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     author = {V. D. Ivashchuk},
     title = {Annihilators in~infinite-dimensional {Grassmann{\textendash}Banach} algebras},
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     volume = {79},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_1_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A family of infinite-dimensional Grassmann–Banach algebras over a complete normalized field $K$ is considered. It is proved that any element $G$ of the family is an associative supercommutative Banach superalgebra over $K$, i. e. $G=G_0\oplus G_1$ with the zero annihilators $G_0^\perp=G_1^\perp=(G_1^{(k)})^\perp=\{0\}$, $k\geqslant2$.

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