Noun
subring (plural subrings)
(algebra) a ring which is contained in a larger ring, such that the multiplication and addition on the former are a restriction of those on the latter.
It turns out that, although ker f is generally not a subring of R since it may not contain the multiplicative identity if S is not the null ring (although the kernel is a subring for nonunital rings). Source: Internet
The first isomorphism theorem for rings states that this quotient ring is naturally isomorphic to the image of f (which is a subring of S). Source: Internet
Examples The most basic example is a ring itself; it is an algebra over its center or any subring lying in the center. Source: Internet
On the other hand, the subset of even integers 2Z does not contain the identity element 1 and thus does not qualify as a subring. Source: Internet
Since the Burnside ring is contained as a finite index subring of the representation ring, one can pass easily from one to the other by extending the coefficients from integers to the rational numbers. Source: Internet
The ring of continuous functions in the previous example is a subring of this ring if X is the real line and R is the field of real numbers. Source: Internet