Cancellation property
In mathematics, the notion of cancellative is a generalization of the notion of invertible. An element a in a magma (M, ∗) has the left cancellation property (or is left-cancellative) if for all b and
Idempotence
Idempotence (UK: /ˌɪdɛmˈpoʊtəns/, US: /ˈaɪdəm-/) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond
Symmetric function
In mathematics, a function of variables is symmetric if its value is the same no matter the order of its arguments. For example, a function of two arguments is a symmetric function if and only if for
Power associativity
In mathematics, specifically in abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity.
Identity element
In mathematics, an identity element, or neutral element, of a binary operation operating on a set is an element of the set that leaves unchanged every element of the set when the operation is applied.
N-ary associativity
In algebra, n-ary associativity is a generalization of the associative law to n-ary operations. Ternary associativity is (abc)de = a(bcd)e = ab(cde), i.e. the string abcde with any three adjacent elem
Quasi-commutative property
In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in specific applications with various definitions.
Flexible algebra
In mathematics, particularly abstract algebra, a binary operation • on a set is flexible if it satisfies the flexible identity: for any two elements a and b of the set. A magma (that is, a set equippe
Alternativity
In abstract algebra, alternativity is a property of a binary operation. A magma G is said to be left alternative if for all and right alternative if for all A magma that is both left and right alterna
Associative property
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, asso
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs
Nilpotent algebra
In mathematics, specifically in ring theory, a nilpotent algebra over a commutative ring is an algebra over a commutative ring, in which for some positive integer n every product containing at least n
Distributive property
In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality is always true in elementary algebra.For example, in elementary arithme
Jacobi identity
In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operat
Anticommutative property
In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is