subring

Noun

Meaning

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.

Phrases with the word

Anagrams

Examples

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

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