The abstract-algebra tag has no wiki summary.

**20**

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**1**answer

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### Infinite Tensor Products

Let $A$ be a commutative ring and $M_i, i \in I$ be a infinite family of $A$-modules. Define their tensor product $\bigotimes_{i \in I} M_i$ to be a representing object of the functor of multilinear ...

**15**

votes

**4**answers

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### Famous exercise from Lang's Algebra

There's a famous story about an exercise from Lang's Algebra that says something along the lines of "pick up a homological algebra book and prove all of the theorems yourself". I cannot find it in ...

**4**

votes

**2**answers

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### when are epimorphisms of algebraic objects surjective?

let $C$ be the category of $\tau$-algebras for some type $\tau$. consider the statements:
every monomorphism is regular.
every epimorphism in C is surjective.
it is easy to see that 1. implies 2. ...

**17**

votes

**2**answers

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### Generalization of the shakehands/condom puzzle?

The classic handshake puzzle goes something like this:
"Given that everyone has a different skin disease, how can you safely shake hands with 3 people when you have only 2 gloves?"
Its common ...

**39**

votes

**5**answers

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### when is A isomorphic to A^3?

this is totally elementary, but I have no idea how to solve it: let $A$ be an abelian group such that $A$ is isomorphic to $A^3$. is then $A$ isomorphic to $A^2$? probably no, but how construct a ...

**0**

votes

**1**answer

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### Newbie boolean algebra question [closed]

The Majority Function is
1: A.B.¬C + A.¬B.C + ¬A.B.C + A.B.C
I can see intuitively that it can be simplified to
2: A.B + A.C + B.C
and thus A.(B + C) + B.C
but how can I use boolean algebra to ...

**3**

votes

**2**answers

764 views

### computation, algebra, logic

So a really simple way of describing a digital computer is to say that it is a device for performing boolean operations. You feed it a bunch of bit strings, which is a description of the problem and ...

**2**

votes

**2**answers

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### Decomposition result for multivariate polynomial

Let $k$ be a positive integer greater than $1$ and suppose that $F \in \mathbb{Z}[x_{1}, \ldots, x_{k}]$.
Can we always find a natural number $n(k)$ and $f_{1}, \ldots f_{n(k)} \in \mathbb{Z}[x]$ ...

**6**

votes

**3**answers

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### Inverses in convolution algebras

Let $G$ be a locally compact totally disconnected group, and to make life easy let's suppose its Haar measure is bi-invariant. Let $C_c(G)$ be the space of locally constant complex functions on $G$ ...

**15**

votes

**6**answers

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### Do convolution and multiplication satisfy any nontrivial algebraic identities?

For (suitable) real- or complex-valued functions f and g on a (suitable) abelian group G, we have two bilinear operations: multiplication -
(f.g)(x) = f(x)g(x),
and convolution -
(f*g)(x) = ...

**32**

votes

**17**answers

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### Canonical examples of algebraic structures

Please list some examples of common examples of algebraic structures. I was thinking answers of the following form.
"When I read about a [insert structure here], I immediately think of [example]."
...