Modules and Algebras

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Questions and Answers

Which of the following is considered a technical question about life?

  • Why do organisms die?
  • What makes humans special?
  • What is living as opposed to non-living? (correct)
  • What is the meaning of life?

What is the range of the number of known and described species?

  • 1.0-1.2 million
  • 1.7-1.8 million (correct)
  • 2.7-2.8 million
  • 2.0-2.2 million

Which of the following evokes a sense of wonder?

  • Attacking shark
  • Migrating Birds
  • Valley of flowers
  • All of the above (correct)

What would happen if you increased the area you observe?

<p>Increase in the range and variety of organisms. (D)</p> Signup and view all the answers

What does each different kind of plant, animal, or organism represent?

<p>A species (D)</p> Signup and view all the answers

Where can living organisms be found?

<p>All of the above (D)</p> Signup and view all the answers

What does the number and types of species in an area refer to?

<p>Biodiversity (A)</p> Signup and view all the answers

Which of the following questions will scientists NOT attempt to answer?

<p>What is the purpose of life? (C)</p> Signup and view all the answers

Which topic was ERNST MAYR's research NOT span?

<p>Zoology (D)</p> Signup and view all the answers

What did a dense forest contain?

<p>Much greater number and kinds of living organisms (C)</p> Signup and view all the answers

Flashcards

Living World

The amazing range of living types and the extraordinary habitats where living organisms are found.

Two Questions About Life

The first is technical, distinguishing living from non-living. The second is philosophical, exploring life's purpose.

Diversity in the Living World

The variety of living organisms in a specific area.

Species

A distinct kind of plant, animal, or organism.

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Biodiversity

The number of species that are known and described.

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Species Range

The range in the number of known and described species.

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Study Notes

  • If G is an abelian group, then G is a ℤ-module.

Z/nZ-modules

  • If G is an abelian group, then G is a ℤ/nℤ-module if n ⋅ x = 0 for all x ∈ G.
  • G = ℤ/nℤ is a ℤ/nℤ-module and a ℤ-module.
  • Let G = {all n-torsion elements of A}, where A is an abelian group, G = {x ∈ A | nx = 0}.

Z-algebras

  • A ring R is a ℤ-algebra if there is a ring homomorphism φ: ℤ → R.

Morphism of Z-algebras:

  • Let R, S be ℤ-algebras.
  • A morphism of ℤ-algebras is a ring homomorphism f: R → S such that the following diagram commutes:
    R
   ^ |
  f | | phi_S
   | v
    S

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