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Finitely Presented Modules over the Steered Algebra in Sage by Michael J. Catamaran ESSAYSubmitted to the College of Liberal Arts and Sciences, Wayne State University, Detroit, Michigan, in partial
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How to fill out finitely presented modules over

How to fill out finitely presented modules over
01
Start by identifying the generators and relations of the module.
02
Write the generators as a free module, M, over a given ring.
03
Use the relations to define a surjective homomorphism from M to the module being filled out.
04
Apply the first isomorphism theorem to show that the module being filled out is isomorphic to the quotient of M by the relations kernel.
Who needs finitely presented modules over?
01
Algebraists and mathematicians studying abstract algebra often need finitely presented modules over to understand the structure of certain algebraic objects.
02
Physicists and engineers working with applications of algebraic structures may also require finitely presented modules over for their research.
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What is finitely presented modules over?
Finitely presented modules are modules that can be generated by finitely many elements subject to certain relations.
Who is required to file finitely presented modules over?
Individuals or organizations that want to study properties of modules in algebra or representation theory.
How to fill out finitely presented modules over?
Fill out the module with a finite number of generators and relations to describe its properties.
What is the purpose of finitely presented modules over?
The purpose is to understand the structure and behavior of modules in various mathematical contexts.
What information must be reported on finitely presented modules over?
Information about the generators and relations that define the module.
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