-
abstract algebra, a
quasigroup is an
algebraic structure that
resembles a
group in the
sense that "division" is
always possible.
Quasigroups differ from groups...
- with
quasigroups,
which are
generalization of
groups in a
different direction; the
operation in a
quasigroup need not be ****ociative but
quasigroups preserve...
- 2004, as a part of his PhD
dissertation entitled Totally Antisymmetric Quasigroups. The Damm
algorithm is
similar to the
Verhoeff algorithm. It too will...
- In mathematics,
especially abstract algebra, loop
theory and
quasigroup theory are
active research areas with many open problems. As in
other areas of...
-
Commonly studied types of
magma include:
Quasigroup: A
magma where division is
always possible. Loop: A
quasigroup with an
identity element. Semigroup: A...
-
generalized to
Moufang loops by
Stephen Gagola III in
recent years. Any
quasigroup satisfying one of the
Moufang identities must, in fact, have an identity...
- a CH-
quasigroup,
introduced by
Manin (1986,
definition 1.3), is a
symmetric quasigroup in
which any
three elements generate an
abelian quasigroup. "CH"...
-
Algebraic structures Group-like
Group Semigroup /
Monoid Rack and
quandle Quasigroup and loop
Abelian group Magma Lie
group Group theory Ring-like Ring Rng...
-
prove that A
forms a
medial quasigroup under this operation. The Bruck–Murdoch-Toyoda
theorem states that
every medial quasigroup is of this form, i.e. is...
- n,R]=[R,R,n]=\{0\}\ .} The
nucleus is an ****ociative
subring of R. A
quasigroup Q is a set with a
binary operation ⋅ : Q × Q → Q {\displaystyle \cdot...
