Given an algebraic structure with a variety of symbols such as addition and multiplication associated with it we can take subalgebras of the structure and reducts of the structure. Subalgebras are produced by taking a subset of the underlying set of the structure. Reducts are produced by taking a subset of the set of symbols associated with the structure.
For example an additive group (S,+) may be a reduct of a field (S,+,*) and an ordered group (S,<=,+) both of which are reducts of an ordered field (S,<=,+,*). A subreduct of a structure is a substructure of the algebraic structure that is both a subalgebra and a reduct because it uses a subset of the underlying set and a subset of the set of symbols used by the structure. The ring of integers is a subreduct of the ordered field of rational numbers.
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