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Get to know Submodule better with 9 real example sentences, the meaning.

Rare word

Submodule in a sentence

Related words

Submodule | Submodules

Submodule meaning

  1. A module making up part of a larger module.
  2. A module contained in a larger module, both over the same ring, such that the ring multiplication in the former is a restriction of that in the latter.

Using Submodule

  • The main meaning on this page is: A module making up part of a larger module. | A module contained in a larger module, both over the same ring, such that the ring multiplication in the former is a restriction of that in the latter.
  • In the example corpus, submodule often appears in combinations such as: submodule of, maximal submodule, proper submodule.

Context around Submodule

  • Average sentence length in these examples: 31.2 words
  • Position in the sentence: 1 start, 4 middle, 4 end
  • Sentence types: 9 statements, 0 questions, 0 exclamations

Often before:

maximal 2× proper 2× invariant 1×

Sentence patterns with Submodule

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

a maximal submodule 1× a maximal submodule of u 1× a right submodule of i 1× a submodule n of 1× proper invariant submodule 1× rings and submodule in the 1× some other submodule n of 1× then every submodule of m 1×

Sentence openings and endings

Common sentence openings:

a submodule n 1× conversely if i 1× for instance if 1× more generally it 1× the notion of 1×

Common sentence endings:

a maximal submodule 1× can be repeated 1× case of modules 1× is again free 1× is not minimal 1× is not simple 1×

Words around Submodule

Just before it in the word index:

submitting 445 submitters 5 submitter 12 submitted 3.526 submittal 3 submits 91

Just after it in the word index:

submodules 7 submultiframe 4 submultiples 2 submunitions 10 submycenaean 2 subnational 21

Similar in corpus frequency:

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

Corpus analysis for Submodule

  • In this selection, "submodule" usually appears in the middle of the sentence. The average example has 31.2 words, and this corpus slice is mostly made up of statements.
  • Around the word, maximal, proper and invariant stand out and add context to how "submodule" is used.
  • Recognizable usage signals include a maximal submodule and a maximal submodule of u. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "submodule" sits close to words such as aab, aamer and aave, which helps place it inside the broader word index.

Example types with submodule

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

If N has a non-zero proper submodule, then this process can be repeated. (14 words)

More generally, it is true that every nonzero finitely generated module has a maximal submodule. (15 words)

If M is a free module over a principal ideal domain R, then every submodule of M is again free. (20 words)

Longer example sentences

If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal. (50 words)

For instance, if U is right R-module, and V is a maximal submodule of U, U·J(R) is contained in V, where U·J(R) denotes all products of elements of J(R) (the "scalars") with elements in U, on the right. (44 words)

The notion of ideal generalises to any Mal'cev algebra (as linear subspace in the case of vector spaces, normal subgroup in the case of groups, two-sided ideals in the case of rings, and submodule in the case of modules ). (41 words)

Example sentences (9)

A submodule N of M is a direct summand of M if there exists some other submodule N′ of M such that M is the internal direct sum of N and N′.

Conversely, if I is not minimal, then there is a non-zero right ideal J properly contained in I. J is a right submodule of I, so I is not simple.

For instance, if U is right R-module, and V is a maximal submodule of U, U·J(R) is contained in V, where U·J(R) denotes all products of elements of J(R) (the "scalars") with elements in U, on the right.

If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

If M is a free module over a principal ideal domain R, then every submodule of M is again free.

If N has a non-zero proper submodule, then this process can be repeated.

If X is a non-zero module over a ring R and the action of G is R-linear then it is said to be * Irreducible if there is no nonzero proper invariant submodule.

More generally, it is true that every nonzero finitely generated module has a maximal submodule.

The notion of ideal generalises to any Mal'cev algebra (as linear subspace in the case of vector spaces, normal subgroup in the case of groups, two-sided ideals in the case of rings, and submodule in the case of modules ).

Common combinations with submodule

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "submodule" in a sentence?
An example: "A submodule N of M is a direct summand of M if there exists some other submodule N′ of M such that M is the internal direct sum of N and N′." This page contains 9 example sentences with the word "submodule" from authentic English texts.
What does "submodule" mean?
Submodule means: A module making up part of a larger module.
How many example sentences with "submodule" are there?
Voorbeeldzinnen.info contains 9 example sentences with "submodule", drawn from a database of millions of English sentences.