👉 In mathematics, a submodule of a module is an ideal in which every element of the module can be expressed as a finite sum of elements of this submodule. This means that for any element m of the module M, there exists a unique submodule N such that mn = 0 for all n ∈ N. For example, consider the ring R[x] with addition defined by (a + b)(x) = ax + bx for all x and a, b in R. The submodule generated by
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What is the definition of Submodule? 🙋
👉 Submodule is a type of a module in mathematics and computer science. In other words, it refers to a smaller module within another larger module or data structure. It's like dividing something into a smaller piece by itself. Submodules are often used to represent mathematical relationships between objects or structures. For example, if we have a matrix M, then its submatrix N is defined as the set of all elements in the row-major or column-major order of M that are located along the main diagonal (
