A linear subspace of an algebra over a field closed under multiplication is a subalgebra. If a unital subalgebra is intended, it must also contain the ambient identity. A closed subalgebra of a normed algebra is closed in the norm topology.
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In the context of algebra, particularly in the study of algebraic structures such as groups, rings, and vector spaces, a **subalgebra** refers to a subset of an algebra that is itself an algebraic structure. The specific properties and definitions can vary depending on the type of algebraic structure being considered.