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Tensor products of idempotent semimodules. An algebraic approach. (English. Russian original) Zbl 0974.46057
Math. Notes 65, No. 4, 479-489 (1999); translation from Mat. Zametki 65, No. 4, 572-585 (1999).
The main purpose of the paper is to define and study some basic properties of a particular type of tensors generated by families of idempotent modules (idempotent “vector spaces” over idempotent semirings of “scalars”). The authors promise future applications to idempotent integration and traces of nuclear operators. This is one of a series of papers on idempotent functional analysis (dealing with semigroups, semirings and semifields with idempotent additive operation).

MSC:
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46M05 Tensor products in functional analysis
46S20 Nonstandard functional analysis
15A69 Multilinear algebra, tensor calculus
15A72 Vector and tensor algebra, theory of invariants
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