Nonassociative right hoops
Rings and Algebras
2021-01-19 v1 Logic
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 is associative and/or commutative. Narhoops with a left unit are proved to have a top element if and only if 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.
Cite
@article{arxiv.1810.06785,
title = {Nonassociative right hoops},
author = {Peter Jipsen and Michael Kinyon},
journal= {arXiv preprint arXiv:1810.06785},
year = {2021}
}