- nonassociative ring
- мат. неассоциативное кольцо, квазикольцо
Большой англо-русский и русско-английский словарь. 2001.
nonassociative ring
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Nonassociative ring — In abstract algebra, a nonassociative ring is a generalization of the concept of ring. A nonassociative ring is a set R with two operations, addition and multiplication, such that: R is an abelian group under addition: a + b = b + a (a + b) + c … Wikipedia
Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia
Lie ring — In mathematics a Lie ring is a structure related to Lie algebras that can arise as a generalisation of Lie algebras, or through the study of the lower central series of groups. Formal definition A Lie ring is defined as a nonassociative ring with … Wikipedia
Division ring — In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a non trivial ring in which every non zero element a has a multiplicative inverse, i.e., an element x with a·x = x·a = 1 … 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
Jordan algebra — In mathematics, a Jordan algebra is defined in abstract algebra as a (usually nonassociative) algebra over a field with multiplication satisfying the following axioms:# xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (Jordan identity)The product… … Wikipedia
E₈ lattice — In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. The normIn… … Wikipedia
List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this … Wikipedia
Associator — In abstract algebra, for a ring or algebra R, the associator is the multilinear map R imes R imes R o R given by: [x,y,z] = (xy)z x(yz).,Just like the commutator measures the degree of noncommutativity, the associator measures the degree of… … Wikipedia
Anneau unitaire — Pour les articles homonymes, voir Anneau. En algèbre générale, un anneau unitaire ou simplement anneau, est un ensemble sur lequel deux opérations satisfont certaines des propriétés de l addition et la multiplication des nombres entiers relatifs … Wikipédia en Français
