Abstract Algebra | Types of rings.

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We define several and give examples of different types of rings which have additional structure.

  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. Randolph College
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Комментарии
Автор

At 3:33, I think you mean "all polynomials with constant coefficient equal to 0" (not those with degree 1 or more). For example, x+1 is a degree 1 polynomial, but is not in x*Z[x].

chaosjunks
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In the last example more term will cancel out inside the brackets involving "a".

harsh
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I really appreciate this video. Thank you

mohithraju
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Very good lecture♡

Please make a video for a Differential geometry course.

enwjvbz
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When did, "There exists a multiplicative identity" stop being a part of the definition of a ring? In my '95 undergrad class it was definitely part of the definition, and a "ring without 1" was called a "rng".

MGSchmahl
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If rings are not supposed to have an identity, then taking any abelian group A one can define a ring structure by setting xy=0 for every x, y in A. Also, every abelian group M is a module over A.

KamalAzhar-tq
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Instead of a having an inverse, how about if it is "only" and adjoint relation. Like a residuated lattice.

tomholroyd
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hello, what do you mean by 3 times 5 =15 =0 inside z15

shebo
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2:44 functions R -> R are a ring under addition and COMPOSITION (he doesn't mean addition and multiplication)

avi