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...

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...

Emerald, and Pokémon Omega Ruby Magma (algebra), an algebraic structure consisting of a set together with a binary operation Magma (cipher), the codename for...

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...

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

types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

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

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...

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...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

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

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation...

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

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

for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics...

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...

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...

"cancellation" can be done in any magma by an element with the cancellation property. Examples include matrix algebras, quaternion algebras, and quasigroups. In an...

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible...

In abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation. A partial...

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

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...

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

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...

(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...

central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the...

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

also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector...