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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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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| author | Hongmei Yao Baodong Zheng |
| author_facet | Hongmei Yao Baodong Zheng |
| author_sort | Hongmei Yao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8db532f682e741e3a1f4acd37bbd9fd4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8db532f682e741e3a1f4acd37bbd9fd42025-02-03T05:50:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/925092925092Zero Triple Product Determined Matrix AlgebrasHongmei Yao0Baodong Zheng1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaLet 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.http://dx.doi.org/10.1155/2012/925092 |
| spellingShingle | Hongmei Yao Baodong Zheng Zero Triple Product Determined Matrix Algebras Journal of Applied Mathematics |
| title | Zero Triple Product Determined Matrix Algebras |
| title_full | Zero Triple Product Determined Matrix Algebras |
| title_fullStr | Zero Triple Product Determined Matrix Algebras |
| title_full_unstemmed | Zero Triple Product Determined Matrix Algebras |
| title_short | Zero Triple Product Determined Matrix Algebras |
| title_sort | zero triple product determined matrix algebras |
| url | http://dx.doi.org/10.1155/2012/925092 |
| work_keys_str_mv | AT hongmeiyao zerotripleproductdeterminedmatrixalgebras AT baodongzheng zerotripleproductdeterminedmatrixalgebras |