Direct Product of Rings

• Let be rings. The direct product is denoted of all ordered -tuples where . Addition and multiplication is defined component-wise (see below) and hence the direct product of rings is a ring.

• The direct product of rings is commutative if and only if each is commutative.

• The direct product of rings has unity if and only if each has unity

Links §

• Fraleigh

• Direct Product of Groups