quasigroup identity
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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
Identity element — In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related… … Wikipedia
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
n-ary group — In mathematics, an n ary group (also n group, polyadic group or multiary group) is a generalization of a group to a set G with a n ary operation instead of a binary operation.[1] The axioms for an n ary group are defined in such a way as to… … 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
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
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
Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… … 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
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
Small Latin squares and quasigroups — Below the Latin squares and quasigroups of some small orders are considered.ize/order 1For size 1 there is 1 Latin square with symbol a and 1 quasigroup with underlying set {a}; it is a group, the trivial group.ize/order 2For size 2 there are 2… … Wikipedia
