On multiplicative equivalences that are totally incompatible with division

An equivalence ∼ upon a loop is said to be multiplicative if it satisfies x ∼ y , u ∼ v ⇒ x u ∼ y v . Let X be a set with elements x ≠ y and let ∼ be the least multiplicative equivalence upon a free loop F ( X ) for which x ∼ y . If a , b ∈ F ( X ) are such that a ≠ b and a ∼ b , then neither a \ c...

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Bibliographic Details
Published in:Algebra universalis 2019-09, Vol.80 (3), p.1-9, Article 32
Main Author: Drápal, Aleš
Format: Article
Language:English
Subjects:
Algebra
Equivalence
Mathematics
Mathematics and Statistics
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Summary:An equivalence ∼ upon a loop is said to be multiplicative if it satisfies x ∼ y , u ∼ v ⇒ x u ∼ y v . Let X be a set with elements x ≠ y and let ∼ be the least multiplicative equivalence upon a free loop F ( X ) for which x ∼ y . If a , b ∈ F ( X ) are such that a ≠ b and a ∼ b , then neither a \ c ∼ b \ c nor c / a ∼ c / b is true, for every c ∈ F ( X ) .
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-019-0605-5