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Ufd is an English word of 3 letters. Below you'll find 10+ example sentences showing how it's used in practice.

Rare word

Ufd in a sentence

Related words

Ufd | Ufds

Ufd meaning

  1. Initialism of unique factorization domain.
  2. Initialism of USB Flash Drive.

Using Ufd

  • The main meaning on this page is: Initialism of unique factorization domain. | Initialism of USB Flash Drive.
  • In the example corpus, ufd often appears in combinations such as: is ufd, be ufd, ufd if.

Context around Ufd

  • Average sentence length in these examples: 20.4 words
  • Position in the sentence: 0 start, 6 middle, 4 end
  • Sentence types: 10 statements, 0 questions, 0 exclamations

Often before:

domain 1× geometry 1×

Often after:

need 1× although 1×

Sentence patterns with Ufd

These short patterns come directly from the example sentences and show how the word is often embedded:

is a ufd 4× is a ufd if and 2× algebraic geometry ufd s arise 1× be a ufd a noetherian 1× be a ufd even if 1× factorization domain ufd although the 1× if the ufd is local 1× is a ufd since in 1×

Sentence openings and endings

Common sentence openings:

a bézout domain 1× a regular local 1× also a dedekind 1× any euclidean domain 1× by iteration a 1× equivalent conditions for 1×

Common sentence endings:

is a ufd 4× a prime element 1× because of smoothness 1× group is trivial 1× is given below 1× is not true 1×

Words around Ufd

Just before it in the word index:

ufcw 13 ufcu 2 ufco 4 ufc 933 ufbu 2 ufas 5

Just after it in the word index:

ufds 2 ufe 2 uff 2 uffi 3 uffington 5 uffish 2

Similar in corpus frequency:

aab 13 aamer 13 aave 13 abdelmadjid 13 abdulkarim 13 abdulsalami 13

Corpus analysis for Ufd

  • In this selection, "ufd" usually appears in the middle of the sentence. The average example has 20.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, domain, geometry, need and although stand out and add context to how "ufd" is used.
  • Recognizable usage signals include is a ufd and is a ufd if and. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "ufd" sits close to words such as aab, aamer and aave, which helps place it inside the broader word index.

Example types with ufd

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

A regular local ring is a UFD. (7 words)

By (2), the ring is a UFD. (7 words)

Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. (15 words)

Longer example sentences

Thus, if, say, k is algebraically closed, then all 's are of the form and the above decomposition corresponds to the Jordan canonical form of f. In algebraic geometry, UFD's arise because of smoothness. (35 words)

Equivalent conditions for a ring to be a UFD A Noetherian integral domain is a UFD if and only if every height 1 prime ideal is principal (a proof is given below). (32 words)

For example, it follows immediately from (2) that a PID is a UFD, since, in a PID, every prime ideal is generated by a prime element. (26 words)

Example sentences (10)

On the other hand, the formal power series ring over a UFD need not be a UFD, even if the UFD is local.

By iteration, a polynomial ring in any number of variables over any UFD (and in particular over a field) is a UFD.

Equivalent conditions for a ring to be a UFD A Noetherian integral domain is a UFD if and only if every height 1 prime ideal is principal (a proof is given below).

A Bézout domain is thus a GCD domain, and (4) gives yet another proof that a PID is a UFD.

Also, a Dedekind domain is a UFD if and only if its ideal class group is trivial.

Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true.

A regular local ring is a UFD.

By (2), the ring is a UFD.

For example, it follows immediately from (2) that a PID is a UFD, since, in a PID, every prime ideal is generated by a prime element.

Thus, if, say, k is algebraically closed, then all 's are of the form and the above decomposition corresponds to the Jordan canonical form of f. In algebraic geometry, UFD's arise because of smoothness.

Common combinations with ufd

These word pairs occur most frequently in English texts:

  • is ufd 7×
  • be ufd 2×
  • ufd if 2×

Frequently asked questions

How do you use "ufd" in a sentence?
An example: "On the other hand, the formal power series ring over a UFD need not be a UFD, even if the UFD is local." This page contains 10+ example sentences with the word "ufd" from authentic English texts.
What does "ufd" mean?
Ufd means: Initialism of unique factorization domain.
How many example sentences with "ufd" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "ufd", drawn from a database of millions of English sentences.