We show that monomial algebras defined by 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 .
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 can be put on their growth rates, for arbitrarily slow unbounded non-decreasing function .
Cite this article
Be'eri Greenfeld, Growth, relations and prime spectrum of monomial algebras. J. Comb. Algebra 4 (2020), no. 1, pp. 61–71DOI 10.4171/JCA/38