Let R be a prime ring of characteristic different from 2,Q_(r) be its right MartindalequotientringandC beitsextendedcentroid,G beanonzero X-generalized skew derivation of R,and S be the set of the evaluations of a mul...Let R be a prime ring of characteristic different from 2,Q_(r) be its right MartindalequotientringandC beitsextendedcentroid,G beanonzero X-generalized skew derivation of R,and S be the set of the evaluations of a multilinear polynomial f(x_(1),...,x_(n))over C with n non-commuting variables.Let u,v∈R be such that uG(x)x+G(x)xv=0 for all x∈S.Then one of the following statements holds:(a)v∈C and there exist a,b,c∈Q_(r) such that G(x)=ax+bxc for any x∈R with(u+v)a=(u+v)b=0;(b)f(x_(1),...,x_(n))2 is central-valued on R and there exists a∈Q r such that G(x)=ax for all x∈R with ua+av=0.展开更多
In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, w...In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well- known theorem on set systems with k-wise E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 （2004）]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.展开更多
基金The work of the second author is partially supported by the National Natural Science Foundation of China(Grant No.10871023).
文摘Let R be a prime ring of characteristic different from 2,Q_(r) be its right MartindalequotientringandC beitsextendedcentroid,G beanonzero X-generalized skew derivation of R,and S be the set of the evaluations of a multilinear polynomial f(x_(1),...,x_(n))over C with n non-commuting variables.Let u,v∈R be such that uG(x)x+G(x)xv=0 for all x∈S.Then one of the following statements holds:(a)v∈C and there exist a,b,c∈Q_(r) such that G(x)=ax+bxc for any x∈R with(u+v)a=(u+v)b=0;(b)f(x_(1),...,x_(n))2 is central-valued on R and there exists a∈Q r such that G(x)=ax for all x∈R with ua+av=0.
文摘In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well- known theorem on set systems with k-wise E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 （2004）]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.
