abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups...
31 KB (3,858 words) - 15:47, 16 July 2024
a CH-quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH"...
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Commonly studied types of magma include: Quasigroup: A magma where division is always possible. Loop: A quasigroup with an identity element. Semigroup: A...
18 KB (1,840 words) - 07:17, 26 August 2024
with quasigroups, which are generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve...
37 KB (4,675 words) - 07:50, 7 June 2024
In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of...
30 KB (3,559 words) - 18:14, 9 February 2024
2004, as a part of his PhD dissertation entitled Totally Antisymmetric Quasigroups. The Damm algorithm is similar to the Verhoeff algorithm. It too will...
12 KB (1,089 words) - 06:55, 4 February 2024
Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic....
26 KB (3,503 words) - 08:47, 10 August 2024
Associator (section Quasigroup theory)
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...
3 KB (488 words) - 02:09, 13 May 2024
then the rows are orthogonal. In fact, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are zeros in...
13 KB (1,868 words) - 23:15, 23 July 2024
Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng...
35 KB (4,447 words) - 08:24, 16 July 2024