Algebraic skew derivations

作者：Chuang Chen Lian; Lee Tsiu Kwen^*

来源：Journal of Algebra, 2012, 353(1): 174-186.

DOI：10.1016/j.jalgebra.2011.12.012

• Prime ring
• Skew derivation
• GPI
• K-polynomial
• K-identity
• cv-Polynomial
• Semi-invariant polynomial
• Invariant polynomial

Let R be a prime ring. C its extended centroid and R-F (resp. Q) its left (resp. symmetric) Martindale quotient ring. Let delta be a sigma-derivation of R, where sigma is an automorphism of R. We show the equivalence of K-polynomials (resp. K-identities) of and cv-polynomials (resp. semi-invariant polynomials) in the Ore extension Q[X; sigma. delta] We prove the existence of K-polynomials of S in certain rather general family of maps. As applications, the following are proved among other things: Consider the expression. phi(x) := Sigma(n)(i=0) a(i)delta(i)(x), where ai is an element of R-F and a(n) not equal 0.
(1) If dim(c) phi(R)C < infinity then either R is a GPI-ring or phi(x) = 0 for all x is an element of R-F.
(2) If phi(R) subset of C then either R is commutative or phi(x) = 0 for all x is an element of R-F.

• 出版日期2012-3-1