are fully coHopfian

USAGE SUMMARY

The phrase "are fully coHopfian" is not correct in standard written English due to the capitalization of "Hopfian." You can use it in a mathematical context when discussing properties of certain algebraic structures, specifically in relation to coHopfian spaces or groups.
Example: "The group G is known to be fully coHopfian, meaning that every injective endomorphism of G is also an automorphism."

⚠ May contain grammatical issues

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

Note that artinian modules are fully coHopfian.

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

If (M) is fully coHopfian, then (M) is artinian.

Bulletin of Mathematical Sciences

Now since (M) is fully coHopfian, we have (M_i = M_n) for each (i ge n).

Bulletin of Mathematical Sciences

Let (M) be fully coHopfian and let (M_1 ge M_2 ge cdots ) be a descending chain of submodules of (M).

Bulletin of Mathematical Sciences

We are fully engaged.

The New York Times

Both are fully adjustable.

The New York Times

Together, they are fully functional.

The New York Times - Arts

But both are fully loaded.

The New York Times - Science

Our rivals are fully funded.

Independent

Our children are fully vaccinated.

The New York Times

Career officials are fully behind it.

The Economist

Expert writing Tips

Best practice

When using the term "are fully coHopfian", ensure that the capitalization of "CoHopfian" is intentional and consistent with the relevant mathematical or scientific convention. If unsure, consult domain-specific style guides or experts to avoid confusion or misinterpretation.

Common error

Avoid inconsistent capitalization when using "are fully coHopfian". Maintain the capitalization of "CoHopfian" throughout your document or publication to ensure clarity and adherence to established conventions.

Linguistic Context

The phrase "are fully coHopfian" functions as an adjectival phrase within mathematical discourse, specifically in the field of module theory. According to Ludwig AI, the capitalization might not be correct in standard English but is valid in specialized mathematical contexts.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "are fully coHopfian" is a specialized term used in mathematics, particularly in module theory, to describe modules with specific properties related to their submodules. Ludwig AI indicates that the capitalization of "CoHopfian" might not be standard in general English, but it's acceptable in a mathematical context. The phrase appears infrequently in broader sources, primarily within scientific publications. When using this term, ensure the capitalization is consistent and appropriate for the mathematical context to avoid confusion. Alternative phrases like "are completely coHopfian" or "are entirely coHopfian" may be considered for clarity, though they should still adhere to mathematical conventions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

are entirely coHopfian

Replaces "fully" with "entirely", offering a synonymous expression with a different emphasis.

are completely coHopfian

Substitutes "fully" with "completely", providing another synonymous expression with a slight shift in tone.

are wholly coHopfian

Replaces "fully" with "wholly", suggesting a total or absolute state of being coHopfian.

are perfectly coHopfian

Replaces "fully" with "perfectly", suggesting an ideal or flawless coHopfian state.

are truly coHopfian

Uses "truly" instead of "fully" to highlight the genuine or authentic nature of being coHopfian.

are thoroughly coHopfian

Replaces "fully" with "thoroughly", implying a comprehensive or exhaustive fulfillment of the coHopfian property.

are intrinsically coHopfian

Emphasizes that the coHopfian property is an inherent or essential characteristic.

are essentially coHopfian

Highlights that the coHopfian nature is fundamental or crucial to their definition.

are fully characterized as coHopfian

Adds "characterized as" to emphasize that the objects possess the coHopfian property in full.

are entirely Hopfian

Removes the "co-" prefix changing the mathematical property and replaces "fully" with "entirely".

FAQs

What does "are fully coHopfian" mean in a mathematical context?

In mathematics, "are fully coHopfian" describes a property where every submodule of a given module is coHopfian. This concept is used in module theory to classify certain types of modules based on their endomorphism properties.

Are there alternatives to using "are fully coHopfian"?

Yes, depending on the context, you can use phrases like "are completely coHopfian" or "are entirely coHopfian" to convey a similar meaning. However, ensure the capitalization is consistent with mathematical conventions.

How do I use "are fully coHopfian" in a sentence?

You can use it in a sentence like: "We call an (R)-module (M) fully coHopfian if every submodule of (M) is coHopfian." Ensure that the context is mathematical and that the capitalization is intentional.

Why is the capitalization of "CoHopfian" important when using "are fully coHopfian"?

The capitalization of "CoHopfian" is important because it is a proper noun referring to a specific mathematical concept. Using incorrect capitalization might cause confusion and misinterpretation among experts in the field.