Journal of Applied Mathematics

Zero Triple Product Determined Matrix Algebras

Hongmei Yao and Baodong Zheng

Full-text: Open access

Abstract

Let A be an algebra over a commutative unital ring C . We say that A is zero triple product determined if for every C -module X and every trilinear map { , , } , the following holds: if { x , y , z } = 0 whenever x y z = 0 , then there exists a C -linear operator T : A 3 X such that x , y , z = T ( x y z ) for all x , y , z A . If the ordinary triple product in the aforementioned definition is replaced by Jordan triple product, then A is called zero Jordan triple product determined. This paper mainly shows that matrix algebra M n ( B ) , n 3 , where B is any commutative unital algebra even different from the above mentioned commutative unital algebra C , is always zero triple product determined, and M n ( F ) , n 3 , where F is any field with ch F 2 , is also zero Jordan triple product determined.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 925092, 18 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495056

Digital Object Identifier
doi:10.1155/2012/925092

Mathematical Reviews number (MathSciNet)
MR2889108

Zentralblatt MATH identifier
1239.16031

Citation

Yao, Hongmei; Zheng, Baodong. Zero Triple Product Determined Matrix Algebras. J. Appl. Math. 2012 (2012), Article ID 925092, 18 pages. doi:10.1155/2012/925092. https://projecteuclid.org/euclid.jam/1355495056


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