👉 In mathematics, an indecomposable object is a mathematical object that cannot be decomposed into smaller objects. In other words, it cannot be made from smaller objects using operations like addition and multiplication. For example, consider the set of all polynomials over a field (which includes integers, rational numbers, real numbers, complex numbers, etc.) with coefficients in a given field. The set of all polynomials is indecomposable because any polynomial can be written as a product of irreducible polynomials