Inverse-Complete Semiring

This paper introduces new algebraic structure inverse-complete semiring (ICS)that generalizes semirings by incorporating a novel treatment of zero and di-vision by zero (DBZ). Unlike conventional semirings, ICS introduces a non-absorbing zero that allows for the existence of multiplicative inverses for allelements, including zero. This paper provides a consistent algebraic foundationfor handling previously undefined operations, such as division by zero, and offerspotential applications in mathematical fields where singularities and undefinedbehavior arise.