Super-additive sequences and algebras of polynomials

Author:
Keith Johnson

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3431-3443

MSC (2010):
Primary 13F20; Secondary 05A10, 11C08

Published electronically:
March 4, 2011

MathSciNet review:
2813375

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a field with discrete valuation and , then an algebra has associated to it a sequence of fractional ideals with consisting of 0 and the leading coefficients of elements of of degree no more than and a sequence of integers with . Combinatorial properties of this integer sequence reflect algebraic properties of , and these are used to identify the degrees of generators of and to characterize finitely generated algebras by a periodicity property of this sequence.

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Additional Information

**Keith Johnson**

Affiliation:
Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada

Email:
johnson@mathstat.dal.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10785-8

Received by editor(s):
May 21, 2010

Received by editor(s) in revised form:
August 30, 2010

Published electronically:
March 4, 2011

Communicated by:
Irena Peeva

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.