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How do you use Semigroup in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.

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Semigroup in a sentence

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Semigroup | Semigroups

Semigroup meaning

Any set for which there is a binary operation that is closed and associative.

Using Semigroup

  • The main meaning on this page is: Any set for which there is a binary operation that is closed and associative.
  • In the example corpus, semigroup often appears in combinations such as: semigroup is, the semigroup, semigroup homomorphism.

Context around Semigroup

  • Average sentence length in these examples: 17.2 words
  • Position in the sentence: 10 start, 9 middle, 1 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

commutative 2× ary 1× arbitrary 1× empty 1× monogenic 1× regular 1× transformation 1× inverse 1× finite 1× periodic 1×

Often after:

homomorphism 3× congruence 2× operation 2× endowed 1× generated 1× shows 1×

Sentence patterns with Semigroup

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

with the semigroup operation 2× 2 ary semigroup is just 1× a commutative semigroup by a 1× a monogenic semigroup is infinite 1× a regular semigroup is inverse 1× a semigroup congruence is 1× a semigroup endowed with 1× a semigroup generated by 1×

Sentence openings and endings

Common sentence openings:

a 2 ary 1× a semigroup congruence 1× a semigroup endowed 1× a semigroup generated 1× a semigroup is 1× a semigroup without 1×

Common sentence endings:

least one idempotent 2× the semigroup operation 2× a semigroup congruence 1× a u semigroup 1× an identity element 1× and maximal subgroups 1×

Words around Semigroup

Just before it in the word index:

semigraphics 6 semigallians 2 semifinals 698 semifinalists 44 semifinalist 34 semifinal 585

Just after it in the word index:

semigroups 6 semikhah 2 semilattice 6 semiliquid 2 semilla 6 semilunar 5

Similar in corpus frequency:

abadi 36 acidification 36 acker 36 actuator 36 affinities 36 aftercare 36

Corpus analysis for Semigroup

  • In this selection, "semigroup" usually appears near the start of the sentence. The average example has 17.2 words, and this corpus slice is mostly made up of statements.
  • Around the word, commutative, ary, arbitrary, homomorphism, congruence and operation stand out and add context to how "semigroup" is used.
  • Recognizable usage signals include with the semigroup operation and 2 ary semigroup is just. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "semigroup" sits close to words such as abadi, acidification and acker, which helps place it inside the broader word index.

Example types with semigroup

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 2-ary semigroup is just a semigroup. (8 words)

Conversely, the kernel of any semigroup homomorphism is a semigroup congruence. (11 words)

Finally, an inverse semigroup with only one idempotent is a group. (11 words)

Longer example sentences

Not every semigroup homomorphism is a monoid homomorphism, since it may not map the identity to the identity of the target monoid, even though the element it maps the identity to will be an identity of the image of the mapping. (41 words)

For each idempotent e of the semigroup there is a unique maximal subgroup containing e. Each maximal subgroup arises in this way, so there is a one-to-one correspondence between idempotents and maximal subgroups. (35 words)

If a monogenic semigroup is infinite then it is isomorphic to the semigroup of positive integers with the operation of addition. (21 words)

Example sentences (20)

A 2-ary semigroup is just a semigroup.

A semigroup congruence is an equivalence relation that is compatible with the semigroup operation.

A semigroup endowed with such an operation is called a U-semigroup.

Conversely, the kernel of any semigroup homomorphism is a semigroup congruence.

Given a homomorphism from an arbitrary semigroup to a semilattice, each inverse image is a (possibly empty) semigroup.

If a monogenic semigroup is infinite then it is isomorphic to the semigroup of positive integers with the operation of addition.

Whenever we take the quotient of a commutative semigroup by a congruence, we get another commutative semigroup.

Alternatively, a regular semigroup is inverse if and only if any two idempotents commute.

Advertentie

A semigroup generated by a single element is said to be monogenic (or cyclic ).

A semigroup is said to be periodic if all of its elements are of finite order.

A semigroup without an identity element can be easily turned into a monoid by just adding an identity element.

A transformation semigroup can be made into an operator monoid by adjoining the identity transformation.

Examples Properties As the last example (a semigroup ) shows, it is possible for (S, ∗) to have several left identities.

Finally, an inverse semigroup with only one idempotent is a group.

For each idempotent e of the semigroup there is a unique maximal subgroup containing e. Each maximal subgroup arises in this way, so there is a one-to-one correspondence between idempotents and maximal subgroups.

For example, every nonempty finite semigroup is periodic, and has a minimal ideal and at least one idempotent.

In order to obtain interesting notion(s), the unary operation must somehow interact with the semigroup operation.

It follows that every nonempty periodic semigroup has at least one idempotent.

It may equivalently be defined as a semigroup homomorphism between groups.

Not every semigroup homomorphism is a monoid homomorphism, since it may not map the identity to the identity of the target monoid, even though the element it maps the identity to will be an identity of the image of the mapping.

Advertentie

Common combinations with semigroup

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "semigroup" in a sentence?
An example: "A 2-ary semigroup is just a semigroup." This page contains 10+ example sentences with the word "semigroup" from authentic English texts.
What does "semigroup" mean?
Semigroup means: Any set for which there is a binary operation that is closed and associative.
How many example sentences with "semigroup" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "semigroup", drawn from a database of millions of English sentences.