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Explore Semisimple through 9 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

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Semisimple in a sentence

Semisimple meaning

  1. In any of several technical senses, decomposable into sub-objects that have a simple structure.
  2. Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.

Using Semisimple

  • The main meaning on this page is: In any of several technical senses, decomposable into sub-objects that have a simple structure. | Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects. | In any of several technical senses, decomposable into sub-objects that have a simple structure.
  • In the example corpus, semisimple often appears in combinations such as: semisimple lie, is semisimple, called semisimple.

Context around Semisimple

  • Average sentence length in these examples: 20.3 words
  • Position in the sentence: 3 start, 3 middle, 3 end
  • Sentence types: 9 statements, 0 questions, 0 exclamations

Often after:

lie 4× rings 1× ring 1×

Sentence patterns with Semisimple

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

algebra is semisimple 1× algebra is semisimple i 1× and a semisimple lie algebra 1× called a semisimple ring if 1× group is semisimple 1× is called semisimple if its 1× it is semisimple as a 1× of a semisimple lie algebra 1×

Sentence openings and endings

Common sentence openings:

a lie algebra 2× conversely it can 1× in particular a 1× semisimple rings a 1× simple and semisimple 1× the problem is 1×

Common sentence endings:

a canonical way 1× algebra is semisimple 1× group is semisimple 1× is not abelian 1× is semisimple i 1× of simple modules 1×

Words around Semisimple

Just before it in the word index:

semisi 6 semis 110 semirom 2 semirings 4 semiring 6 semiregular 2

Just after it in the word index:

semiskilled 2 semisolid 2 semisonic 2 semistate 4 semistocles 2 semistructured 2

Similar in corpus frequency:

aakash 12 aanholt 12 aardwolf 12 abadan 12 abati 12 abcc 12

Corpus analysis for Semisimple

  • In this selection, "semisimple" usually appears near the start of the sentence. The average example has 20.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, lie, rings and ring stand out and add context to how "semisimple" is used.
  • Recognizable usage signals include algebra is semisimple and algebra is semisimple i. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "semisimple" sits close to words such as aakash, aanholt and aardwolf, which helps place it inside the broader word index.

Example types with semisimple

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

In particular, a simple Lie algebra is semisimple. (8 words)

A Lie algebra is called semisimple if its radical is zero. (11 words)

The semisimple Lie groups have a deep theory, building on the compact case. (13 words)

Longer example sentences

A Lie algebra is solvable if and only if Classification The Levi decomposition expresses an arbitrary Lie algebra as a semidirect sum of its solvable radical and a semisimple Lie algebra, almost in a canonical way. (36 words)

Semisimple rings A ring is called a semisimple ring if it is semisimple as a left module (or right module) over itself; i.e., a direct sum of simple modules. (30 words)

Conversely, it can be proven that any semisimple Lie algebra is the direct sum of its minimal ideals, which are canonically determined simple Lie algebras. (25 words)

Example sentences (9)

Semisimple rings A ring is called a semisimple ring if it is semisimple as a left module (or right module) over itself; i.e., a direct sum of simple modules.

When the ground field F has characteristic zero, any finite-dimensional representation of a semisimple Lie algebra is semisimple (i.

A Lie algebra is called semisimple if its radical is zero.

A Lie algebra is solvable if and only if Classification The Levi decomposition expresses an arbitrary Lie algebra as a semidirect sum of its solvable radical and a semisimple Lie algebra, almost in a canonical way.

Conversely, it can be proven that any semisimple Lie algebra is the direct sum of its minimal ideals, which are canonically determined simple Lie algebras.

In particular, a simple Lie algebra is semisimple.

Simple and semisimple A Lie algebra is " simple " if it has no non-trivial ideals and is not abelian.

The problem is to prove that the 2-layer of the centralizer of an involution in a simple group is semisimple.

The semisimple Lie groups have a deep theory, building on the compact case.

Common combinations with semisimple

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "semisimple" in a sentence?
An example: "Semisimple rings A ring is called a semisimple ring if it is semisimple as a left module (or right module) over itself; i.e., a direct sum of simple modules." This page contains 9 example sentences with the word "semisimple" from authentic English texts.
What does "semisimple" mean?
Semisimple means: In any of several technical senses, decomposable into sub-objects that have a simple structure.
How many example sentences with "semisimple" are there?
Voorbeeldzinnen.info contains 9 example sentences with "semisimple", drawn from a database of millions of English sentences.