19 citations · 201 across the 54 of their papers we have counts for
6 papers · 1 filter
Special identities for the pre-Jordan product in the free dendriform algebra
Murray R. Bremner, Sara Madariaga
Pre-Jordan algebras were introduced recently in analogy with pre-Lie algebras. A pre-Jordan algebra is a vector space with a bilinear multiplication such that the p…
The Cayley-Dickson process for dialgebras
R. Felipe-Sosa, R. Felipe, J. Sanchez-Ortega +2
We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley-Dickson doubli…
On Kruskal's theorem that every 3 x 3 x 3 array has rank at most 5
Murray R. Bremner, Jiaxiong Hu
In the first part of this paper, we consider 3 x 3 x 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal's theorem that the maximum rank is 5. In…
Higher identities for the ternary commutator
Murray R. Bremner, Luiz A. Peresi
We use computer algebra to study polynomial identities for the trilinear operation [a,b,c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a,…
Canonical forms of small tensors over F_2
Murray R. Bremner, Jiaxiong Hu
We consider multidimensional arrays with at most 27 entries over the field with two elements, and their equivalence classes for the action of the direct product of general linear g…
Algebras, dialgebras, and polynomial identities
Murray R. Bremner
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We di…