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June 1, 2026International Journal of Algebra and Computation0 citations

On the growth of modules

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BGBe’eri GreenfeldEZEfim Zelmanov

Key Points

  • The aim is to explore how certain functions can be realized as growth functions of modules with specific algebraic properties.
  • Investigated necessary conditions for functions to qualify as growth functions.
  • Examined relationships between growth functions and algebraic properties like concavity and polynomial growth.
  • Explored regular elements and polynomial identities in the context of modules.
  • Identified conditions under which functions can serve as growth functions of modules.
  • Showed that concavity and polynomial growth relate directly to specific algebraic properties.
  • Demonstrated the implications of polynomial identities on growth functions.

Abstract

Growth functions of modules encode important algebraic properties. Conversely, we address the inverse problem of realizing functions that satisfy necessary conditions as growth functions of modules with specific algebraic properties, exploring concavity, polynomial growth, regular elements and polynomial identities.

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Cite This Study

Greenfeld et al. (2026) studied this question.

synapsesocial.com/papers/6a1d226d02fbce9130638206https://doi.org/10.1142/s0218196726400072
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