On exp(tA) with A satisfying a polynomial

Rings with a setwise polynomial-like condition

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

On the polar derivative of a polynomial

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

On Szeged Polynomial of a Graph

Representation Theory of Noetherian Hopf Algebras Satisfying a Polynomial Identity

A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelian-by-nite groups, nite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some common homological and representation-theoretic features of these algebras are described, with some indica...

Satisfying Subtype Inequalities in Polynomial Space

This paper studies the complexity of type inference in-calculus with subtyping. Type inference is equivalent to solving systems of subtype inequalities. We consider simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a PSPACE upper bound. Together with the known lower bound, this result settles completely the complexity of type inference ov...