Abstract:
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=G0⊕G1 with the zero annihilators G⊥0=G⊥1=(G(k)1)⊥={0}, k⩾2.
Citation:
V. D. Ivashchuk, “Annihilators in infinite-dimensional Grassmann–Banach algebras”, TMF, 79:1 (1989), 30–40; Theoret. and Math. Phys., 79:1 (1989), 361–368
This publication is cited in the following 8 articles:
John Howie, Steven Duplij, Ali Mostafazadeh, Masaki Yasue, Vladimir Ivashchuk, Concise Encyclopedia of Supersymmetry, 2004, 201
A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, Theoret. and Math. Phys., 97:2 (1993), 1267–1272
V. D. Ivashchuk, “Tensor Banach algebras of projective type. I”, Theoret. and Math. Phys., 91:1 (1992), 336–345
V. D. Ivashchuk, “Tensor Banach algebras of projective type. II. The $l_1$ case”, Theoret. and Math. Phys., 91:2 (1992), 462–473
A. Yu. Khrennikov, “On the theory of infinite-dimensional superspace: reflexive Banach supermodules”, Russian Acad. Sci. Sb. Math., 77:2 (1994), 331–350
A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238
Vladimir Pestov, “Ground Algebras for superanalysis”, Reports on Mathematical Physics, 29:3 (1991), 275
V. D. Ivashchuk, “Invertibility of elements in infinite-dimensional Grassmann–Banach algebras”, Theoret. and Math. Phys., 84:1 (1990), 682–688
Citation in format AMSBIB
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