Get to know Subring better with 7 real example sentences, the meaning.
Subring meaning
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. When rings are required to have a multiplicative identity (as is standard in most branches of algebra), the subring must also have the same multiplicative identity as the larger ring.
Using Subring
- The main meaning on this page is: 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. When rings are required to have a multiplicative identity (as is standard in most branches of algebra), the subring must also have the same multiplicative identity as the larger ring.
- In the example corpus, subring often appears in combinations such as: subring of, is subring.
Context around Subring
- Average sentence length in these examples: 29.9 words
- Position in the sentence: 0 start, 4 middle, 3 end
- Sentence types: 7 statements, 0 questions, 0 exclamations
Corpus analysis for Subring
- In this selection, "subring" usually appears in the middle of the sentence. The average example has 29.9 words, and this corpus slice is mostly made up of statements.
- Around the word, index and lying stand out and add context to how "subring" is used.
- Recognizable usage signals include as a subring and finite index subring of the. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "subring" sits close to words such as aaba, aafc and aaib, which helps place it inside the broader word index.
Example types with subring
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Examples The most basic example is a ring itself; it is an algebra over its center or any subring lying in the center. (23 words)
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. (25 words)
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). (25 words)
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). (38 words)
To give a less trivial example, * The ring of rational functions generated by x and y/x n over a field k is a subring of the field k(x,y) in only two variables. (35 words)
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. (34 words)
Example sentences (7)
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).
Examples The most basic example is a ring itself; it is an algebra over its center or any subring lying in the center.
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.
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.
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).
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.
To give a less trivial example, * The ring of rational functions generated by x and y/x n over a field k is a subring of the field k(x,y) in only two variables.
Common combinations with subring
These word pairs occur most frequently in English texts:
- subring of 5×
- is subring 4×