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arXiv · 1810.06785

Nonassociative right hoops

Peter Jipsen·Michael Kinyon
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Abstract

The class of nonassociative right hoops, or narhoops for short, is defined as a subclass of right-residuated magmas, and is shown to be a variety. These algebras generalize both right quasigroups and right hoops, and we characterize the subvarieties in which the operation $x\sqcap y=(x / y)y$ is associative and/or commutative. Narhoops with a left unit are proved to have a top element if and only if $\sqcap$ is commutative, and their congruences are determined by the equivalence class of the left unit. We also show that the four identities defining narhoops are independent.

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Peter Jipsen, Michael Kinyon. 2018-10-16. Nonassociative right hoops. https://doi.org/10.1007/s00012-019-0618-0

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