Abstract
Tensor product decomposition of algebras is known to be non-unique in many cases. But we know that a ⊕-indecomposable, finite-dimensional C -algebra A has an essentially unique tensor factorization A = A 1 ⊗ ⋯ ⊗ A r into non-trivial, ⊗-indecomposable factors A i . Thus the semiring of isomorphism classes of finite-dimensional C -algebras is a polynomial semiring N [ X ]. 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
