Let be an arbitrary commutative ring with identity, the general linear Lie algebra over , the diagonal subalgebra of . In case 2 is a unit of , all subalgebras of containing are determined and their derivations are given. In case 2 is not a unit partial results are given.
This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
2000 Mathematics Subject Classification: 11T06, 13P10.A theorem of S.D. Cohen gives a characterization for Dickson polynomials of the second kind that permutes the elements of a finite field of cardinality the square of the characteristic. Here, a different proof is presented for this result.Research supported by the CERES program of the Ministry of Education, Research and Youth, contract nr. 39/2002.