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Tagged with magma solution-verification
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Magma $(\mathbb R,*)$ with a binary operation $\;a*b=a+b-2a^2b^2$
Let $(\mathbb R, *)$ be a magma with a binary operation:
$$a*b=a+b-2a^2b^2$$ Prove
$(a)$ the binary operation is commutative, but not associative,
$(b)$ $0$ is a neutral element for that ...
- 4,670
2
votes
0
answers
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operation on set proof
Consider the operation ⊥ defined by placing, for every $x,y\in Z$
$x⊥y=x+|y|$, Check Associativity and Commutativity. Is there a Identity element in $Z$?
My proof:
Associativity
$x⊥(y⊥z)=(x⊥y)⊥z$
$x⊥(...
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A right group is the direct product of a group and a right zero semigroup.
This is (most of) Exercise 2.6.6 of Howie's "Fundamentals of Semigroup Theory". The first part is here.
The Details:
Let $S$ be a semigroup.
Definition 1: We call $S$ right simple if $\...
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The direct product $G\times E$ of a group $G$ with a right zero semigroup $E$ is a right group.
This is part of Exercise 2.6.6 of Howie's "Fundamentals of Semigroup Theory". I apologise in advance if this is a duplicate.
The Details:
Let $S$ be a semigroup.
Definition 1: We call $S$ right ...
- 45.8k
1
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1
answer
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Proving that $f(A+B)=f(A)+f(B).$
Let $X$ and $Y$ denote magmas, and suppose $f : X \rightarrow Y$ is homomorphism. Then I think that for all $A,B \subseteq X$, we have $f(A+B)=f(A)+f(B).$ However, I'm not happy with my:
Proof. The ...
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