In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure...

Look up magma or magmatic in Wiktionary, the free dictionary. Magma is molten rock found under the Earth's surface. Magma may also refer to: Magma (character)...

form magmas, to which the concepts concerning magmas, as well those concerning sets, apply. We can add additional constraints on the algebraic structure...

In abstract algebra, a medial magma or medial groupoid is a magma or groupoid (that is, a set with a binary operation) that satisfies the identity (x...

additionally use unary operations. Magma or groupoid: S and a single binary operation over S. Semigroup: an associative magma. Monoid: a semigroup with identity...

nonassociative algebras are flexible: Alternative algebras Lie algebras Jordan algebras (which are commutative) Okubo algebras In the world of magmas, there is...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

In abstract algebra, alternativity is a property of a binary operation. A magma G is said to be left alternative if ( x x ) y = x ( x y ) {\displaystyle...

children's game of rock, paper, scissors. Such magmas give rise to non-associative algebras. A magma which is both commutative and associative is a commutative...

Representation theory of Hopf algebras General Associative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup Nonassociative...

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

small number of general-purpose computer algebra systems. Significant systems include Axiom, GAP, Maxima, Magma, Maple, Mathematica, and SageMath. In the...

and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics...

operation – Repeated application of an operation to a sequence Magma (algebra) – Algebraic structure with a binary operation Operator (programming) – Basic...

groups, rings, and fields, there are many other algebraic structures studied by algebra. They include magmas, semigroups, monoids, abelian groups, commutative...

version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB". The originator and leader of the SageMath...

cancellability) is a generalization of the notion of invertibility. An element a in a magma (M, ∗) has the left cancellation property (or is left-cancellative) if for...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

graph Magma (algebra) Ore algebra Ore condition Ore's conjecture Ore extension Ore number Ore's theorem Schwartz–Zippel lemma Universal algebra "Øystein...

quasigroup (Q, ∗) is a non-empty set Q with a binary operation ∗ (that is, a magma, indicating that a quasigroup has to satisfy the closure property), obeying...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

algebra for Jordan algebras. List of algebras Commutative non-associative magmas, which give rise to non-associative algebras Schafer 1995, Chapter 1. Schafer...

and z in the semigroup. Semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without...

free Lie algebra can be given in terms of a Hall set, which is a particular kind of subset inside the free magma on X. Elements of the free magma are binary...

(xy)z =x(yz). Any magma that satisfies these two rectangular identities and idempotence is therefore a rectangular band. So any magma that satisfies both...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

mathematics, and more specifically in abstract algebra, a rng (or non-unital ring or pseudo-ring) is an algebraic structure satisfying the same properties as...

abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity. An algebra (or more generally a magma) is said...

is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique...