# Linked Questions

3answers
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### Homework - Prove that a given set is a group [duplicate]

I have a homework question and I don't know how to approach this exercise. The exercise is the following: Let's suppose $G$ is a set with binary function * defined for its members, which is: ...
1answer
1k views

### Finding the Right Inverses and Right Identity of a Group [duplicate]

Possible Duplicate: Right identity and Right inverse implies a group Let $(G,*)$ be a binary structure that has the following properties: 1) The binary operation $*$ is associative. 2) There ...
0answers
57 views

### Is $G$ a group under those conditions? [duplicate]

Let $G$ be a set and $*:G\times G \rightarrow G$ an operation with: (i) $(G,*)$ is associative (ii) There is a $f \in G$ with $f*a=a$ for all $a \in G$ (iii) For every $a \in G$ exists a $b \in G$ ...
0answers
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1answer
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### Proof of brauer's lemma, $eRe$ being a division ring.

On page 1 of this article, the author proves the following claim: Brauer's Lemma: Let $K$ be a minimal left ideal of a ring $R$, with $K^2 \not= 0$. Then $K=Re$ where $e^2=e \in R$, and $eRe$ is a ...
1answer
176 views

### Prove that (G,*) is a group.

G is a monoid and satisfies the right inverse law. Show that G is a group. I tried next: It is obviously sufficient to show that G satisfies left inverse law. (I use $a'$ notation for $a$ inverse.) We ...
1answer
101 views

### Do those 'groups' have a name?

Is there a name for 'groups' that only have a neutral element on the right and an inverse for each element on the right ? If there is, does that name also hold for a neutral elt on the right and an ...
2answers
156 views

### If a magma M is both a semigroup and a quasigroup, is it necessarily a group?

If a magma which has an identity element is also a semigroup and a quasigroup, it can be shown that this is indeed a group. I'm looking for a counter example: a magma which is a quasigroup (for every ...
1answer
81 views

### Is a semigroup with unique right identity and left inverse a group?

We know that a semigroup with a right identity and right inverse for all elements is a group (e.g. see here). Symmetrically, also a left identity together with a left inverse implies a group. We also ...

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