Note on length and multiplicity of modules over two-dimensional regular local rings

Key Points

• The aim is to establish bounds on the Buchsbaum-Rim multiplicity for modules over two-dimensional regular local rings and outline conditions for achieving these bounds.
• Derived lower and upper bounds on Buchsbaum-Rim multiplicity.
• Analyzed finitely generated torsion-free modules.
• Derived formulae for the multiplicity of integrally closed modules.
• Provided explicit lower and upper bounds on multiplicity.
• Identified conditions under which modules attain these multiplicity bounds.
• Created formulae relating to the multiplicity of integrally closed modules.