Racks and quandles information

In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams...

another Racking focus, a photography technique Rack of ribs, a food item made up of a set of ribs Rack of lamb, a cut of lamb meat Racks and quandles, concepts...

have certain properties of algebraic and combinatorial interest. They occur in the study of racks and quandles. For any nonnegative integer n, the n-th...

theories Operadic algebra Diagrammatic algebra Quantum field theory Racks and quandles Mathematics portal Science portal Technology portal Coherent states...

Hyperbolic volume Kontsevich invariant Linking number Milnor invariants Racks and quandles and Biquandle Ropelength Seifert surface Self-linking number Signature...

operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations...

mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition...

A monoid is an algebraic structure intermediate between semigroups and groups, and is a semigroup having an identity element, thus obeying all but one...

known, one may use the Euclidean algorithm and extended Euclidean algorithm to compute greatest common divisors and Bézout's identity. In particular, the existence...

Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or...

of irreducible elements, uniquely up to order and units. Important examples of UFDs are the integers and polynomial rings in one or more variables with...

multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear". The...

equivalent to "field" ("corps") is used for both commutative and noncommutative cases, and the distinction between the two cases is made by adding qualificatives...

algebra and algebraic geometry, homological algebra, and algebraic topology. One example is the close relationship between homogeneous polynomials and projective...

which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite...

commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization...

integrally closed, they are unique factorization domains and Dedekind domains. All Euclidean domains and all fields are principal ideal domains. Principal ideal...

is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain...

domain. In fact a Dedekind domain is a unique factorization domain (UFD) if and only if it is a PID. In the 19th century it became a common technique to...

which is both a unital associative algebra and a counital coassociative coalgebra.: 46  The algebraic and coalgebraic structures are made compatible with...

multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of K). The addition and multiplication...

the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the...

order and vice versa. Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any...

Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however...