An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation
In 1949 M.~Sholander proved that every medial cancellation groupoid can be embedded into a medial quasigroup. In this paper we prove that it is also true for $n$-ary cancellation groupoids, namely, every medial cancellation $n$-ary groupoid can be embedded into a medial $n$-ary quasigroup.
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2015-12-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/119 |
| Summary: | In 1949 M.~Sholander proved that every medial cancellation groupoid can be embedded into a medial quasigroup. In this paper we prove that it is also true for $n$-ary cancellation groupoids, namely, every medial cancellation $n$-ary groupoid can be embedded into a medial $n$-ary quasigroup.
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| ISSN: | 1829-1163 |