A **subring** is a concept in abstract algebra, particularly in the study of ring theory. A subring is a subset of a ring that is itself a ring under the same operations (addition and multiplication) defined in the larger ring. To formally define a subring, let’s consider a ring \( R \) with two binary operations: addition \( + \) and multiplication \( \cdot \).
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A subset closed under addition, additive inverses and multiplication, with the induced operations. Under the unital convention used here it also contains the identity of . A subring of an integral domain is again an integral domain. The ring of invariants is one example: fixed elements remain fixed under all ring operations.