ABSTRACT

A subring of a ring R is a subset containing 0 ,1, that is a ring under the given + and · o f R. To verify that T is a subring o f R we need only check that (T , + ) is subgroup of (R, + ) and that (Γ , ·, 1) is a subm onoid o f (R , ·, 1), for distributivity in T is a direct consequence of distributivity in R. This observation is enhanced in exercise 4.