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Tagged with magma abelian-groups
3
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Commutative subtraction
It is well known that subtraction is not commutative in general.
However, it is commutative in some groups: $\mathbb I$, $\mathbb C_2$, $\mathbb K_4$.
I am trying to understand the logic.
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- 1,120
0
votes
1
answer
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Build abelian group containing a set $K$ under an associative, commutative operation $*$ with an identity but the inverses are not always in $K$.
We are given a set K of elements and an operation * . For every element in the set, there exists an inverse element (not necessarily in the set). There are three (additional) rules:
1) K contains e (...
- 184
2
votes
2
answers
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Proof of closure and identity element for $a * b = ab - a - b + 2$
For real numbers $x > 1$, which forms the set $G$, it is given that the operation on $a,b$, being $a\ast b$, results in $ab - a - b + 2$ (where $ab$ is the ordinary multiplication of $a$ and $b$).
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