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An equivalence \(\sim \) upon a loop is said to be multiplicative if it satisfies \(x\sim y\), \(u \sim v \Rightarrow xu \sim yv\). Let X be a set with… Click to show full abstract
An equivalence \(\sim \) upon a loop is said to be multiplicative if it satisfies \(x\sim y\), \(u \sim v \Rightarrow xu \sim yv\). Let X be a set with elements \(x\ne y\) and let \(\sim \) be the least multiplicative equivalence upon a free loop F(X) for which \(x\sim y\). If \(a,b\in F(X)\) are such that \(a\ne b\) and \(a\sim b\), then neither \(a\backslash c \sim b\backslash c\) nor \(c/a \sim c/b\) is true, for every \(c\in F(X)\).
Keywords:
incompatible division;
multiplicative equivalences;
equivalences totally;
sim;
totally incompatible
Journal Title: Algebra universalis
Year Published: 2019
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Journal Title: Algebra universalis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!