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2-normed algebras. I. (English) Zbl 1263.46008
Summary, modified: As shown by S. N. Lal et al. [Progr. Math., Varanasi 35, No. 1–2, 27–31 (2001; Zbl 1186.46009)], the class of 2-normed real algebras, defined by N. Mohammad and A. H. Siddiqi [Aligarh Bull. Math. 12, 51–60 (1989; Zbl 0751.46030)] either is void or contains only trivial algebras. In this paper, new definitions of real or complex 2-normed algebras and 2-Banach algebras are proposed. Several examples of such algebras are given.

MSC:
46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
46H05 General theory of topological algebras
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