Thus the set X⨯Y becomes a ring with these operations and it is called the product ring. The identity element of the product ring with respect to the addition is obviously (0,0) where 0 and 0 are identity elements of addition in the rings X and Y!, respectively.

I put a bet on the winning horse.

Completion of an identifiable stage of maintenance such as removing an aircraft engine for repair or storage.

How could the flogger of urchins be otherwise than animated and joyous?