What Do You Know About Simple Modules?

10 Questions | Total Attempts: 105

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What Do You Know About Simple Modules? - Quiz

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.


Questions and Answers
  • 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

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