Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф：...Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.展开更多
Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving comm...Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B2n （F）.展开更多
Abstract Let F be a field, and let G be the standard Borel subgroup of the symplectie group Sp（2m, F）. In this paper, we characterize the bijective maps φ： G -- G satisfying φ[x, y] = [φ（x）, φ（y）].
基金Supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015Item PA010)National Natural Science Foundation of China(Grant Nos.11526123 and 11401273)
文摘Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.
文摘Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B2n （F）.
文摘Abstract Let F be a field, and let G be the standard Borel subgroup of the symplectie group Sp（2m, F）. In this paper, we characterize the bijective maps φ： G -- G satisfying φ[x, y] = [φ（x）, φ（y）].
