Zero Triple Product Determined Matrix Algebras
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/925092 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |