Subalgebra refers to the subset of an algebra that forms an itself an algebra under the same operations. There are several synonyms for subalgebra, including quotient algebra, subring, submodule, subfield, and subvector space. A quotient algebra is a type of algebraic structure formed by separating a fixed ideal from a larger algebra. Subring refers to a subset of a ring that satisfies the same ring conditions, while a submodule is a subset of a module over a ring which is closed under the module operations. A subfield is a subset of a field that is itself a field, while a subvector space is a subset of a vector space that satisfies the same vector space conditions as the larger space.