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://www.armjmath.sci.am/index.php/ajm/article/view/119 |
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doaj-8b0fae7c66744972909d0346a53f75402020-11-25T00:10:52ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-12-0172An Embedding Theorem for Medial $\bf n$-ary Groupoid with CancellationSergey Davidov0Department of Mathematics and Mechanics, Yerevan State University Alek Manoogian 1, 0025, Yerevan, Armenia 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. http://www.armjmath.sci.am/index.php/ajm/article/view/119 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sergey Davidov |
| spellingShingle |
Sergey Davidov An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation Armenian Journal of Mathematics |
| author_facet |
Sergey Davidov |
| author_sort |
Sergey Davidov |
| title |
An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation |
| title_short |
An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation |
| title_full |
An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation |
| title_fullStr |
An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation |
| title_full_unstemmed |
An Embedding Theorem for Medial $\bf n$-ary Groupoid with Cancellation |
| title_sort |
embedding theorem for medial $\bf n$-ary groupoid with cancellation |
| publisher |
Republic of Armenia National Academy of Sciences |
| series |
Armenian Journal of Mathematics |
| issn |
1829-1163 |
| publishDate |
2015-12-01 |
| description |
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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| url |
http://www.armjmath.sci.am/index.php/ajm/article/view/119 |
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AT sergeydavidov anembeddingtheoremformedialbfnarygroupoidwithcancellation AT sergeydavidov embeddingtheoremformedialbfnarygroupoidwithcancellation |
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