JournalsjcaVol. 4, No. 1pp. 61–71

Growth, relations and prime spectrum of monomial algebras

  • Be'eri Greenfeld

    Bar-Ilan University, Ramat-Gan, Israel
Growth, relations and prime spectrum of monomial algebras cover
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Abstract

We show that monomial algebras defined by rnr_n relations of each degree can (under mild assumptions) be mapped onto prime monomial algebras with prescribed growth functions tightly bounded by any function growing slower than rnr_n.

Using the same method, we are able to construct finitely generated, prime monomial algebras with GK-dimension 2 admitting arbitrarily long chains of prime ideals, providing an answer to a question of Bergman from 1989. Unlike the previously known examples, our algebras are computable, concretely constructed and concrete upper bounds of the form n2f(n)n^2f(n) can be put on their growth rates, for arbitrarily slow unbounded non-decreasing function ff.

Cite this article

Be'eri Greenfeld, Growth, relations and prime spectrum of monomial algebras. J. Comb. Algebra 4 (2020), no. 1, pp. 61–71

DOI 10.4171/JCA/38