1. a subset of a ring that is itself a ring under the same operations
Usage: mathematics

Examples

• The set of even integers forms a subring of the ring of all integers.
• In abstract algebra, we study how subrings relate to their parent rings.
• The polynomial ring over the rationals contains many interesting subrings.
• To prove something is a subring, you must verify closure under addition and multiplication.
• The intersection of two subrings is always a subring.
• Matrix rings often contain diagonal subrings as proper subsets.