1,980 research outputs found
A dichotomy result for prime algebras of Gelfand-Kirillov dimension two
Let be an uncountable field. We show that a finitely generated prime
Goldie -algebra of quadratic growth is either primitive or satisfies a
polynomial identity, answering a question of Small in the affirmative.Comment: 10 page
Noetherian algebras over algebraically closed fields
Let be an uncountable algebraically closed field and let be a
countably generated left Noetherian -algebra. Then we show that is left Noetherian for any field extension of . We conclude that all
subfields of the quotient division algebra of a countably generated left
Noetherian domain over are finitely generated extensions of . We give
examples which show that need not remain left Noetherian if the
hypotheses are weakened.Comment: 10 page
A problem around Mahler functions
Let be a field of characteristic zero and and be two
multiplicatively independent positive integers. We prove the following result
that was conjectured by Loxton and van der Poorten during the Eighties: a power
series satisfies both a - and a -Mahler type functional
equation if and only if it is a rational function.Comment: 52 page
The Positivity Set of a Recurrence Sequence
We consider real sequences that satisfy a linear recurrence with
constant coefficients. We show that the density of the positivity set of such a
sequence always exists. In the special case where the sequence has no positive
dominating characteristic root, we establish that the density is positive.
Furthermore, we determine the values that can occur as density of such a
positivity set, both for the special case just mentioned and in general
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