Unique tensor factorization of loop-resistant algebras over a field of finite characteristic

JOURNAL OF ALGEBRA

卷:251

Article

Nüsken, M

关键词: tensor product of algebras;    unique factorization;   

DOI  :  10.1006/jabr.2001.9126

来源: Elsevier

【 摘 要 】

Tensor product decomposition of algebras is known to be non-unique in many cases. But we know that a circle plus-indecomposable, finite-dimensional C-algebra A has an essentially unique tensor factorization A = At circle times (...) circle times A(r) into non-trivial, circle times-indecomposable factors A(i). Thus the semiring of isomorphism classes of finite-dimensional C-algebras is a polynomial semiring N[H]. Moreover, the field C 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. (C) 2002 Elsevier Science (USA).

【 授权许可】

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