| Title:
|
Antiassociative groupoids (English) |
| Author:
|
Braitt, Milton |
| Author:
|
Hobby, David |
| Author:
|
Silberger, Donald |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
142 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
27-46 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a groupoid $\langle G, \star \rangle $, and $k \geq 3$, we say that $G$ is antiassociative if an only if for all $x_1, x_2, x_3 \in G$, $(x_1 \star x_2) \star x_3$ and $x_1 \star (x_2 \star x_3)$ are never equal. Generalizing this, $\langle G, \star \rangle $ is $k$-antiassociative if and only if for all $x_1, x_2, \ldots , x_k \in G$, any two distinct expressions made by putting parentheses in $x_1 \star x_2 \star x_3 \star \cdots \star x_k$ are never equal. \endgraf We prove that for every $k \geq 3$, there exist finite groupoids that are $k$-antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal. (English) |
| Keyword:
|
groupoid |
| Keyword:
|
unification |
| MSC:
|
08A99 |
| MSC:
|
20N02 |
| MSC:
|
68Q99 |
| MSC:
|
68R15 |
| MSC:
|
68T15 |
| idZBL:
|
Zbl 06738568 |
| idMR:
|
MR3619985 |
| DOI:
|
10.21136/MB.2017.0006-15 |
| . |
| Date available:
|
2017-02-21T17:20:50Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146007 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
