The Extension Theorem for Bi-invariant Weights over Frobenius Rings and Frobenius Bimodules

TL;DR

This paper establishes a sufficient condition under which bi-invariant weights on Frobenius bimodules satisfy the extension property, generalizing to finite Frobenius rings and analyzing complex-valued functions as modules over semigroup rings.

Contribution

It introduces a new sufficient condition for the extension property of bi-invariant weights on Frobenius bimodules, extending previous results to a broader class of rings.

Findings

Condition applies to finite Frobenius rings

Complex-valued functions viewed as modules over semigroup rings

Generalizes extension property to broader algebraic structures

Abstract

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the semigroup ring of the multiplicative semigroup of the coefficient ring.