Rectangular loops (Q2724045)
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scientific article; zbMATH DE number 1615363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rectangular loops |
scientific article; zbMATH DE number 1615363 |
Statements
8 July 2001
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groupoids
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rectangular loops
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axiomatization
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independent axioms
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word problems
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identities
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Rectangular loops (English)
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A groupoid \(S\) is a rectangular loop if it is isomorphic to the direct product of a left zero semigroup, a loop and a right zero semigroup. The problem of axiomatization of the class of all rectangular loops is considered. \textit{R. A. Knoebel} [Algebra Univers. 3, 147-151 (1973; Zbl 0273.08004)] gave an axiom system for rectangular loops consisting of 21 identities. In this paper a simpler equivalent system of 12 identities is obtained. Some properties of rectangular loops are derived.
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