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Jordan left derivations in infinite matrix rings

Zhang Daochang, Ma Leiming, Hu Jianping, Sun Chaochao

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230150

Let R be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over R are equal to zero and demonstrate that a left derivation d:T→T in the infinite upper triangular matrix ring T is determined by left derivations dj in R(j=1,2,…) satisfying […] for any […], where [formula]. The similar results about Jordan left derivations are also obtained when R is 2-torsion free.