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Unique Tensor Factorization of Loop-Resistant Algebras over a Field of Finite Characteristic

✍ Scribed by Michael Nüsken

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
171 KB
Volume
251
Category
Article
ISSN
0021-8693

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✦ Synopsis

Tensor product decomposition of algebras is known to be non-unique in many cases. But we know that a ⊕-indecomposable, finite-dimensional -algebra A has an essentially unique tensor factorization

Thus the semiring of isomorphism classes of finite-dimensional -algebras is a polynomial semiring . Moreover, the field of complex numbers can be replaced by an arbitrary (not necessarily algebraically closed) field of characteristic zero if we restrict ourselves to split algebras.

Here, we show that the above result still holds in finite characteristics if we only consider loop-resistant algebras.  2002 Elsevier Science (USA)

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