We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. Types of algebras that are studied include alternative, flexible, quadratic and involutive algebras, as well as algebras obtained by the Cayley–Dickson doubling process. Our results include precise criteria for von-Neumann finiteness and reversibility of involutive algebras in terms of isomorphism types of their 3-dimensional subalgebras.

中文翻译：

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某些非缔合代数的冯-诺依曼有限性和可逆性

我们研究了某些类别的非缔合代数中冯-诺依曼有限性和可逆性的标准。研究的代数类型包括替代代数，柔性代数，二次代数和对合代数，以及通过Cayley-Dickson倍增过程获得的代数。我们的研究结果包括对合代数的von-Neumann有限性和可逆性的精确标准，这取决于它们的3维子代数的同构类型。