What Do You Know About Simple Modules?
Despite the fact that not all simple modules have a simple submodule, every simple module is generated by one element. Meanwhile, the idea of simple modules is particularly connected in the ring theory field of mathematics. In group theory, simple modules are analogous to simple groups. They also create building blocks for the modules of finite length.
- 1.
If every cyclic submodule generated by a non-zero element of a module equals that module, what is it?- A.
Long
- B.
Simple
- C.
Cyclic
- D.
Proper
- 2.
What is a collection of finitary operations on a carrier set?
- A.
Modular structure
- B.
Algebraic structure
- C.
Structural abstract
- D.
Simple module
- 3.
Which is not an abstract algebra?
- A.
Slopes
- B.
Modules
- C.
Vector spaces
- D.
Lattice
- 4.
What is a unified way of expressing properties and constructions that are similar for various structures?
- A.
Ring theory
- B.
Group theory
- C.
Category theory
- D.
Abstract theory
- 5.
How many elements has a cyclic module?
- A.
1
- B.
2
- C.
3
- D.
4
- E.
5
- 6.
Which kind of modules is direct summands of free modules?
- A.
Projective
- B.
Simple
- C.
Cyclic
- D.
Noetherain
- 7.
Which module embeds into its algebraic dual?
- A.
Noetherain
- B.
Torsionless
- C.
Torsion-free
- D.
Reducible
- 8.
Which is a completely reducible module also called?
- A.
Semi simple
- B.
Simple
- C.
Torsional
- D.
Zero
- 9.
Which is a non-zero module that cannot be written as a direct sum of two non-zero submodules?
- A.
Indecomposable
- B.
Noetherain
- C.
Torsion
- D.
Simple
- 10.
Which module satisfies the ascending chain condition on submodules?
- A.
Noetherain
- B.
Indecompossable
- C.
Decomposable
- D.
Torsion
Questions: 12 | Attempts: 5566173 | Last updated: Mar 22, 2022
-
Sample QuestionWho said "The universe can not be read until we learn the language and become familiar with the characters in which it is writte"?
Questions: 8 | Attempts: 1579790 | Last updated: Mar 22, 2022
-
Sample QuestionWhat is the square root of 49?
Questions: 15 | Attempts: 452320 | Last updated: Mar 22, 2022
-
Sample QuestionHow much should you tip on a $30 restaurant bill if you tip 20%?
- Cartography Quizzes
- Civics Quizzes
- Economics Quizzes
- El112 Quizzes
- English Quizzes
- Geography Quizzes
- History Quizzes
- Humanities Quizzes
- Law Quizzes
- Linguistics Quizzes
- Logic Quizzes
- Philosophy Quizzes
- Political Science Quizzes
- Politics Quizzes
- Science Quizzes
- Social Science Quizzes
- Sociology Quizzes
Back to top