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2004•Czech digital mathematics libraryOpen access

Tensor products of sequential effect algebras

Stanley Gudder

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Abstract

A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined.It is first shown that the tensor product of a Boolean algebra with an arbitrary SEA exists.We then characterize pairs of SEA's that admit a tensor product.As a corollary we show that a pair of commutative SEA's admit a tensor product if they admit a bimorphism.

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A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined.It is first shown that the tensor product of a Boolean algebra with an arbitrary SEA exists.We then characterize pairs of SEA's that admit a tensor product.As a corollary we show that a pair of commutative SEA's admit a tensor product if they admit a bimorphism.

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Available abstract

A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined.It is first shown that the tensor product of a Boolean algebra with an arbitrary SEA exists.We then characterize pairs of SEA's that admit a tensor product.As a corollary we show that a pair of commutative SEA's admit a tensor product if they admit a bimorphism.

Key concepts: Tensor product of algebras, Tensor product, Tensor product of modules, Tensor product of Hilbert spaces, Mathematics, Tensor algebra, Corollary, Algebra over a field

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