abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups...

a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH"...

Commonly studied types of magma include: Quasigroup: A magma where division is always possible. Loop: A quasigroup with an identity element. Semigroup: A...

with quasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve...

In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of...

2004, as a part of his PhD dissertation entitled Totally Antisymmetric Quasigroups. The Damm algorithm is similar to the Verhoeff algorithm. It too will...

Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic....

n,R]=[R,R,n]=\{0\}\ .} The nucleus is an associative subring of R. A quasigroup Q is a set with a binary operation ⋅ : Q × Q → Q {\displaystyle \cdot...

then the rows are orthogonal. In fact, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are zeros in...

Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...