On a locally finite variety of idempotent groupoids with arbitrarily large simple groupoids (Q802588)
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scientific article; zbMATH DE number 3891442
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a locally finite variety of idempotent groupoids with arbitrarily large simple groupoids |
scientific article; zbMATH DE number 3891442 |
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On a locally finite variety of idempotent groupoids with arbitrarily large simple groupoids (English)
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1984
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The variety generated by the commutative idempotent groupoid \(M=\{1,2,3\}\) with \(1\circ 2=2\), \(1\circ 3=3\) and \(2\circ 3=1\) is proved to contain a simple groupoid of cardinality k for any cardinal number k; the variety is generated by any of these simple groupoids. It is also proved that there are exactly three essentially binary and exactly 84 essentially ternary polynomials on M.
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commutative idempotent groupoid
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variety
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simple groupoids
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essentially ternary polynomials
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