Below you will find example sentences with "direct product". The examples show how this phrase is used in natural context and which words often surround it.
Direct Product in a sentence
Corpus data
- Displayed example sentences: 17
- Discovered as a combination around: direct
- Corpus frequency in the collocation scan: 11
- Phrase length: 2 words
- Average sentence length: 22.5 words
Sentence profile
- Phrase position: 8 start, 7 middle, 2 end
- Sentence types: 17 statements, 0 questions, 0 exclamations
Corpus analysis
- The phrase "direct product" has 2 words and usually appears near the start in these examples. The average sentence has 22.5 words and is mostly made up of statements.
- Around this phrase, patterns and context words such as a finite direct product may also, a semi direct product among groups, sum, vector and spaces stand out.
- In the phrase index, this combination connects with direct sum, new product, product gdp, direct sum, direct flights and direct knowledge, linking the page to nearby combinations.
Example types with direct product
This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:
The direct product is a special case of the semidirect product. (11 words)
Similarly, the definition of the direct product of modules is subsumed here. (12 words)
A "finite" direct product may also be viewed as a direct sum of ideals. (14 words)
For example, the Schur–Zassenhaus theorem implies the existence of a semi-direct product among groups of order 6; there are two such products, one of which is a direct product, and the other a dihedral group. (37 words)
Direct product and direct sum main The direct product of vector spaces and the direct sum of vector spaces are two ways of combining an indexed family of vector spaces into a new vector space. (35 words)
Our Connecticut-based operation provides direct product support across the state and nationwide in partnership with frontline social services providers such as food pantries, homeless shelters, underserved school communities, and health clinics. (32 words)
Example sentences (17)
Direct product and direct sum main The direct product of vector spaces and the direct sum of vector spaces are two ways of combining an indexed family of vector spaces into a new vector space.
Internal and external direct product seeAlso Some authors draw a distinction between an internal direct product and an external direct product.
The direct sum and direct product differ only for infinite indices, where the elements of a direct sum are zero for all but for a finite number of entries.
For example, the Schur–Zassenhaus theorem implies the existence of a semi-direct product among groups of order 6; there are two such products, one of which is a direct product, and the other a dihedral group.
Thus e.g. Z/12 is the direct product of Z/3 and Z/4, but not the direct product of Z/6 and Z/2.
A "finite" direct product may also be viewed as a direct sum of ideals.
The direct product of finitely many rings coincides with the direct sum of rings.
In this case, the splitting lemma shows that every semidirect product is a direct product.
The direct product is a special case of the semidirect product.
The team quickly learns that the Ishimura is overrun with aggressive alien creatures called Necromorphs, a direct product of the reanimated corpses of dead crew members.
Our Connecticut-based operation provides direct product support across the state and nationwide in partnership with frontline social services providers such as food pantries, homeless shelters, underserved school communities, and health clinics.
Huawei also has words to say about how the amended Foreign Direct Product Rules effectively throw global industries into chaos.
Generally, an interval in mathematics corresponds to an ordered pair (x,y) taken from the direct product R × R of real numbers with itself.
In Jubilees 1:20, Belial’s appearance continues to support the notion that sin is a direct product of his influence.
Similarly, the definition of the direct product of modules is subsumed here.
The fundamental theorem of abelian groups states that every finitely generated abelian group is the direct product of finitely many finite primary cyclic and infinite cyclic groups.
With a direct product, we get some natural group homomorphisms for free: the projection maps : called the coordinate functions.