We study the ring Γ of all functions N → K, endowed with the usual convolution product. Γ, which we call the ring of number-theoretic functions, is an inverse limit of the “truncations” Γn = { f ∈ Γ ∀m > n : f(m) = 0 } . Each Γn is a zero-dimensional, finitely generated K-algebra, which may be expressed as the quotient of a finitely generated polynomial ring with a stable (after reversing the o...

We propose a method for computing the radical of an arbitrary ideal in the polynomial ring in n variables over a perfect field of characteristic p > 0. In our method Buchberger’s algorithm is performed once in n variables and a Gröbner basis conversion algorithm is performed at most dn logp de times in 2n variables, where d is the maximum of total degrees of generators of the ideal and 3. Next ...

Let K be a field and let A be a finitely generated prime K-algebra. We generalize a result of Smith and Zhang, showing that if A is not PI and does not have a locally nilpotent ideal, then the extended centre of A has transcendence degree at most GKdim(A) − 2 over K. As a consequence, we are able to show that if A is a prime K-algebra of quadratic growth, then either the extended centre is a fi...