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"...

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

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

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

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

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...

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

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

a⁻¹ ∗ (a ∗ c) which implies b = c by associativity. For example, every quasigroup, and thus every group, is cancellative. To say that an element a in a...