a central division

USAGE SUMMARY

The phrase "a central division" is correct and usable in written English.
It can be used to refer to a primary or main section within an organization, structure, or system. Example: "The company has established a central division to oversee all marketing efforts across its various branches."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

We define the genus (mathbf{gen}(D)) of (D) to be the collection of classes ([D^{prime }] in mathrm{Br}(K)), where (D^{prime }) is a central division (K -algebra having the same maximal subfields as (D).

Bulletin of Mathematical Sciences

Their Theorem 2.2 provides estimates for (vert mathbf{gen}^{prime }(D) vert ) of a central division algebra (D) over (K = k(x)) of a prime exponent (p ne mathrm{char} k) similar to those given in Theorem 3.3.

Bulletin of Mathematical Sciences

The following theorem provides an estimation of the size of (mathbf{gen}(D) cap _nmathrm{Br}(K)) for a central division (K -algebra (D) of exponent (n) in certain situations.

Bulletin of Mathematical Sciences

One of the results announced in [5] states that if (K) is a finitely generated field, then the genus (mathbf{gen}(D)) of a central division (K -algebra (D) of degree (n) prime to (mathrm{char}, K -algebrate.

Bulletin of Mathematical Sciences

This isomorphism can be described as follows: if ([mathcal D ] in _nmathrm{Br}(mathcal K )_{{ v }}) is represented by a central division (mathcal K )-algebra (mathcal D ), then the residue division algebra (overline{mathcal{D }}) is central over (overline{mathcal{K }}) and (nu ([mathcal D ]) = [overline{mathcal{D }}]).

Bulletin of Mathematical Sciences

In [14], Krashen and MacKinnie defined the genus (mathbf{gen}^{prime }(D)) of a central division (K -algebra (D) as the collection of ([D^{prime }] in mathrm{Br}(K -algebra the same finite-Dimensionas splitheng fields as (D) (collectionathbf{gen}^{prime }(D) subset mathbf{gen}(D))).

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

end{aligned}Now, since (vert mathbf{gen}(D) vert = 1) for any central division algebra (D) of exponent two over a global field (k), Theorem 3.5 yields the following.

Bulletin of Mathematical Sciences

(2) If (vert mathbf{gen}(D) vert = 1) for any central division (k -algebra (D) of exponent 2, then the same is true for any central division (k -algebrabra of exponent 2.  .

Bulletin of Mathematical Sciences

Then for any central division (K -algebra (D) of exponent 2, we have (vert mathbf{gen}(D) vert = 1).

Bulletin of Mathematical Sciences

If (vert mathbf{gen}(D) vert = 1) for any central division (k -algebra (D) of exponent 2, then the same is true for any central division (k -algebrabra of exponent 2. Let (k) be either a finite fielD of charactexponent(ne 2) or a number field, and (K = k(x_1, ldothenx_r)) be a finithey generated purely transamedental extensisn of (k).

Bulletin of Mathematical Sciences

Then (vert mathbf{gen}(D) vert = 1) for any central division (K -algebra (D) of exponent 2. As we already mentioned, Theorem 3 of [5] asserts that if (K -algebranitely generateD field, then fof any cexponentivision (K)-algebra (D) of degree (n) prime to (mathrm{char} K), the genus (mathbf{gen}(D)) is finite.

Bulletin of Mathematical Sciences

Expert writing Tips

Best practice

When referring to a specific, named division, ensure proper capitalization (e.g., "the Central Division of Pathology"). However, when using the phrase generically, lowercase "central division" is appropriate.

Common error

Avoid overuse of "central division" when a simpler term like "main department" or "core unit" would suffice, especially in informal writing.

Linguistic Context

The phrase "a central division" functions primarily as a noun phrase, identifying a specific, core part or unit within an organization or structure. As Ludwig AI confirms, it's generally grammatically correct. The examples provided by Ludwig show its common usage in both scientific and news contexts.

Expression frequency: Rare

Frequent in

Science

40%

News & Media

40%

Wiki

20%

Less common in

Formal & Business

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

The phrase "a central division" is a noun phrase used to identify a core organizational unit. Ludwig AI analysis confirms its grammatical correctness. While examples are somewhat rare, it appears in both scientific and news contexts, suggesting a neutral formality level. When using "a central division", proper capitalization depends on whether you're referring to a specifically named division or using the term generically. Consider using alternatives like "a main department" or "a core unit" for broader applicability.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a main department

Replaces "division" with a more general term for an organizational unit.

the central branch

Replaces "division" with "branch", implying a part of a larger organization.

a core unit

Emphasizes the central or essential nature of the division.

the main subdivision

Uses "subdivision" to indicate a division within a larger entity.

a primary sector

Uses "sector" as a synonym for "division", suitable in some contexts.

the core segment

Employs "segment" as a synonym, often used in business contexts.

a key section

Highlights the importance of the division within a larger structure.

a pivotal group

Indicates that the division plays a crucial role.

a strategic arm

Suggests that the division is integral to the organization's strategy.

a fundamental component

Emphasizes the division's role as a basic building block.

FAQs

How can I use "a central division" in a sentence?

You can use "a central division" to refer to a main organizational unit within a company, team, or structure. For example, "The company established a central division to handle all marketing activities."

What's a good alternative to "a central division"?

Alternatives include "a main department", "a core unit", or "a primary sector", depending on the context.

When should I capitalize "central division"?

Capitalize "Central Division" when referring to a specifically named division within an organization. Otherwise, use lowercase for the generic term "a central division".

Is "central division" formal or informal?

The phrase "central division" is generally considered neutral to professional. The formality depends more on the surrounding context and the specific use case.