On the growth of modules

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.