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 ^^ y = (x/y)y is associative and/or commutative. Narhoops with a left unit are proved to be integral if and only if ^ is commutative, and their congruences are determined by the equivalence class of the left unit. We also prove that the four identities defining narhoops are independent.
P. Jipsen and M. Kinyon, Nonassociative right hoops, Algebras and Lattices in Hawai'i: honoring Ralph Freese, Bill Lampe, and JB Nation (2018), 54-60
Kira Adaricheva, William DeMeo, Jennifer Hyndman (the editors)
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