TL;DR
This paper explores the properties of isoperimetric profiles in algebras, examining how they change under different algebraic constructions and their connection to Gelfand-Kirillov dimension.
Contribution
It provides new insights into the behavior of isoperimetric profiles in algebras and their relation to algebraic dimensions, extending Gromov's initial work.
Findings
Analysis of isoperimetric profile behavior under algebraic constructions
Relationship established between isoperimetric profile and Gelfand-Kirillov dimension
New theoretical results on algebraic invariants
Abstract
Isoperimetric profile in algebras was first introduced by Gromov. We study the behavior of the isoperimetric profile under various ring theoretic constructions and its relation with the Gelfand-Kirillov dimension.
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