Tensor products of idempotent semimodules. An algebraic approach. (English. Russian original) Zbl 0974.46057

Litvinov, G. L.; Maslov, V. P.; Shpiz, G. B.

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).

Reviewer: Todor D.Todorov (San Luis Obispo)

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

Keywords:

idempotent ring; idempotent module; tensors; families of idempotent modules; idempotent integration; traces of nuclear operators; idempotent functional analysis

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