Short Exact Sequence
A "Short Exact Sequence" is a concept in homological algebra that describes a sequence of three abelian groups or modules connected by two homomorphisms. It is written as 0 \to A \to B \to C \to 0, where the image of each homomorphism is equal to the kernel of the next. This structure ensures that the sequence captures essential properties of the groups involved.
In this sequence, A injects into B, and B surjects onto C. The exactness at each point indicates that the mappings preserve certain algebraic structures, allowing mathematicians to study relationships between different algebraic objects.