We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Zero Triple Product Determined Matrix Algebras.
- Authors
Hongmei Yao; Baodong Zheng
- 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 xyz = 0, then there exists a C-linear operator T : A3 → X such that {x, y, z} = T(xyz) 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 Mn(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 Mn(F), n = 3, where F is any field with chF≠ 2, is also zero Jordan triple product determined.
- Subjects
MATRICES (Mathematics); COMMUTATIVE rings; RING theory; MATHEMATICAL mappings; LINEAR operators; ALGEBRAIC field theory
- Publication
Journal of Applied Mathematics, 2012, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2012/925092