Maps Determined by Action on Square-Zero Elements

摘要

Let M _n (R) be the algebra of all n × n matrices over a unital commutative ring R with 6 invertible, and let X be an R-module. It is shown that if a symmetric bilinear map {·, ·}: M _n (R) × M _n (R) → X satisfies the condition that {u, u} = 0 whenever u 2 = 0, then there exists a linear map f: [sl _n (R)]2 → X such that {x, y} = f(x ○ y),  x, y  sl _n (R), where sl _n (R) denotes the subset of M _n (R) of all matrices of trace zero.View full textDownload full textKey WordsBilinear maps, Square-zero determined algebras, Zero product determined algebras2010 Mathematics Subject Classification15A03, 15A04, 15A27, 15A99Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.606860