Let be an algebra over a commutative unital ring . We say that is zero triple product determined if for every -module and every trilinear map , the following holds: if whenever , then there exists a -linear operator such that for all . If the ordinary triple product in the aforementioned definition is replaced by Jordan triple product, then is called zero Jordan triple product determined. This paper mainly shows that matrix algebra , , where B is any commutative unital algebra even different from the above mentioned commutative unital algebra , is always zero triple product determined, and , , where F is any field with ch, is also zero Jordan triple product determined.
Hongmei Yao. Baodong Zheng. "Zero Triple Product Determined Matrix Algebras." J. Appl. Math. 2012 1 - 18, 2012. https://doi.org/10.1155/2012/925092