The algorithm can be extended to handle matrix products over other algebraic structures beyond the ring of integers by adapting the methodology to suit the specific properties of the target algebraic structure. For example, when dealing with matrices over a field, such as real numbers or complex numbers, the algorithm can be modified to incorporate the properties of fields, such as the existence of multiplicative inverses for non-zero elements.
To handle matrix products over a general algebraic structure, one approach could be to define the necessary operations and properties of the structure, such as closure under multiplication and the existence of additive and multiplicative identities. The algorithm can then be tailored to work within the constraints and properties of the specific algebraic structure, ensuring correct matrix products and efficient error correction.
By customizing the algorithm to accommodate different algebraic structures, such as fields or groups, the versatility and applicability of the algorithm can be expanded to a wide range of mathematical contexts beyond just the ring of integers.