The endomorphism ring consists of the -module homomorphisms , with pointwise addition and composition as multiplication.
A nonzero module is a brick when every endomorphism is either zero or an isomorphism. Equivalently, its endomorphism ring is a division ring.
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The **endomorphism ring** of a mathematical structure, such as a module, vector space, or algebraic object, is a way to study the set of all endomorphisms of that structure with respect to a specific operation—usually addition and composition.