Planar ternary ring, the Glossary

Table of Contents

1. 24 relations: Affine plane (incidence geometry), Algebraic structure, Analytic geometry, Associative property, Cartesian coordinate system, Commutative property, Ergebnisse der Mathematik und ihrer Grenzgebiete, Field (mathematics), Group (mathematics), Homogeneous coordinates, Identity element, Incidence matrix, Linear equation, Marshall Hall (mathematician), Mathematics, Near-field (mathematics), Non-Desarguesian plane, Projective plane, Quasifield, Quasigroup, Ring (mathematics), Semifield, Springer Science+Business Media, Transactions of the American Mathematical Society.

Affine plane (incidence geometry)

In geometry, an affine plane is a system of points and lines that satisfy the following axioms.

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Algebraic structure

In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. Planar ternary ring and algebraic structure are algebraic structures.

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Analytic geometry

In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Associative property

In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result.

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Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Ergebnisse der Mathematik und ihrer Grenzgebiete

Ergebnisse der Mathematik und ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics is a series of scholarly monographs published by Springer Science+Business Media.

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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 the corresponding operations on rational and real numbers. Planar ternary ring and field (mathematics) are algebraic structures.

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Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element. Planar ternary ring and group (mathematics) are algebraic structures.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. Planar ternary ring and homogeneous coordinates are projective geometry.

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Identity element

In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied.

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Incidence matrix

In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b.

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Marshall Hall (mathematician)

Marshall Hall Jr. (17 September 1910 – 4 July 1990) was an American mathematician who made significant contributions to group theory and combinatorics.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Near-field (mathematics)

In mathematics, a near-field is an algebraic structure similar to a division ring, except that it has only one of the two distributive laws. Planar ternary ring and near-field (mathematics) are algebraic structures and projective geometry.

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Non-Desarguesian plane

In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. Planar ternary ring and non-Desarguesian plane are projective geometry.

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Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane. Planar ternary ring and projective plane are projective geometry.

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Quasifield

In mathematics, a quasifield is an algebraic structure (Q,+,\cdot) where + and \cdot are binary operations on Q, much like a division ring, but with some weaker conditions. Planar ternary ring and quasifield are projective geometry.

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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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Ring (mathematics)

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. Planar ternary ring and ring (mathematics) are algebraic structures.

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Semifield

In mathematics, a semifield is an algebraic structure with two binary operations, addition and multiplication, which is similar to a field, but with some axioms relaxed. Planar ternary ring and semifield are algebraic structures.

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Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

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References

[1] https://en.wikipedia.org/wiki/Planar_ternary_ring

Also known as Ternary field, Ternary ring.