Quasigroup

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• Quasigroup — In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that division is always possible. Quasigroups differ from groups mainly in that they need not be associative. A quasigroup with …   Wikipedia

• quasigroup — noun An algebraic structure, resembling a group, whose arithmetic may not be associative …   Wiktionary

• Problems in loop theory and quasigroup theory — In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many …   Wikipedia

• CH-quasigroup — In mathematics, a CH quasigroup, introduced by Manin (1986, definition 1.3), is a symmetric quasigroup in which any three elements generate an abelian quasigroup. CH stands for cubic hypersurface. References Manin, Yuri Ivanovich (1986) [1972],… …   Wikipedia

• Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

• Algebraic structure — In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The… …   Wikipedia

• Hyperbolic quaternion — In mathematics, a hyperbolic quaternion is a mathematical concept first suggested by Alexander MacFarlane in 1891 in a speech to the American Association for the Advancement of Science. The idea was criticized for its failure to conform to… …   Wikipedia

• List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

• Isotopy of loops — Isotopy of quasigroups = Let (Q,cdot) and (P,circ) be quasigroups. A quasigroup homotopy from Q to P is a triple (α, β, γ) of maps from Q to P such that :alpha(x)circeta(y) = gamma(xcdot y),for all x , y in Q . A quasigroup homomorphism is just… …   Wikipedia

• Medial — This article is about medial in mathematics. For other uses, see medial (disambiguation). Contents 1 Medial magmas 2 Bruck Toyoda theorem 3 Generalizations 4 See also …   Wikipedia

• Moufang loop — In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by Ruth Moufang. Contents 1 Definition 2 Examples 3 Properties …   Wikipedia