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53 relations: Absorbing element, Abstract algebra, Addition, Additive inverse, Associative property, Bijection, Binary operation, Cancellation property, Closure (mathematics), Codomain, Commutative ring, Completely regular semigroup, Determinant, Division ring, Domain of a function, Field (mathematics), Function composition, Galois connection, Generalized inverse, Green's relations, Group (mathematics), Idempotence, Identity element, Identity function, If and only if, Inverse function, Inverse semigroup, Invertible matrix, Involution (mathematics), Latin square property, Least squares, Magma (algebra), Matrix multiplication, Monoid, Moore–Penrose inverse, Multiplication, Multiplicative inverse, Oxford University Press, Partial function, Quasigroup, Rank (linear algebra), Real number, Regression analysis, Semigroup, Semigroup Forum, Semigroup with involution, Set (mathematics), Special classes of semigroups, Square matrix, Symmetric inverse semigroup, ..., Transformation semigroup, Unit (ring theory), 0. Expand index (3 more) »
Absorbing element
In mathematics, an absorbing element is a special type of element of a set with respect to a binary operation on that set.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Addition
Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.
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Additive inverse
In mathematics, the additive inverse of a number is the number that, when added to, yields zero.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Binary operation
In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.
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Cancellation property
In mathematics, the notion of cancellative is a generalization of the notion of invertible.
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
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Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
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Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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Completely regular semigroup
In mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Division ring
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).
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Generalized inverse
In mathematics, and in particular, algebra, a generalized inverse of an element x is an element y that has some properties of an inverse element but not necessarily all of them.
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Green's relations
In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Idempotence
Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Inverse semigroup
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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Latin square property
In mathematics, the Latin square property is an elementary property of all groups and the defining property of quasigroups.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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Magma (algebra)
In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.
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Moore–Penrose inverse
In mathematics, and in particular linear algebra, a pseudoinverse of a matrix is a generalization of the inverse matrix.
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Multiplication
Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Partial function
In mathematics, a partial function from X to Y (written as or) is a function, for some subset X ′ of X.
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Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible.
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Rank (linear algebra)
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semigroup Forum
Semigroup Forum (print, electronic) is a mathematics research journal published by Springer.
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Semigroup with involution
In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application "cancelling itself out", and the same interaction law with the binary operation as in the case of the group inverse.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Special classes of semigroups
In mathematics, a semigroup is a nonempty set together with an associative binary operation.
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Symmetric inverse semigroup
In abstract algebra, the set of all partial bijections on a set X (one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is \mathcal_X or \mathcal_X In general \mathcal_X is not commutative.
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Transformation semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of functions from a set to itself that is closed under function composition.
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Unit (ring theory)
In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.
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0
0 (zero) is both a number and the numerical digit used to represent that number in numerals.
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I-semigroup, Inverse (ring theory), Inverse elements, Invertible, Left inverse element, Left invertible, One-sided inverse, Quasi-inverse, Right invertible, U-semigroup, ⁻¹.
References
[1] https://en.wikipedia.org/wiki/Inverse_element
