-
abstract algebra, a
quasigroup is an
algebraic structure that
resembles a
group in the
sense that "division" is
always possible.
Quasigroups differ from groups...
-
Commonly studied types of
magma include:
Quasigroup: A
magma where division is
always possible. Loop: A
quasigroup with an
identity element. Semigroup: A...
- 2004, as a part of his PhD
dissertation entitled Totally Antisymmetric Quasigroups. The Damm
algorithm is
similar to the
Verhoeff algorithm. It too will...
-
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...
-
Algebraic structures Group-like
Group Semigroup /
Monoid Rack and
quandle Quasigroup and loop
Abelian group Magma Lie
group Group theory Ring-like Ring Rng...
- with
quasigroups,
which are
generalization of
groups in a
different direction; the
operation in a
quasigroup need not be ****ociative 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...
-
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"...
-
unique for all a and all b (the
Latin square property) is a
quasigroup. In a
quasigroup,
division in this
sense is
always possible, even
without an identity...
