A double groupoid is a mathematical structure that generalizes the concept of a groupoid. To understand what a double groupoid is, it helps to first clarify what a groupoid is. ### Groupoid A **groupoid** consists of a set of objects and a set of morphisms (arrows) between these objects satisfying certain axioms. Specifically: - Each morphism has a source and target object.

Kleene algebra is a mathematical structure used in theoretical computer science, formal language theory, and algebra. It is named after the mathematician Stephen Kleene, who made significant contributions to the foundations of automata theory and formal languages. Kleene algebra consists of a set equipped with certain operations and axioms that support reasoning about the properties of regular languages and automata.

In algebra, particularly in the context of ring theory, the term "rng" (pronounced "ring") is an abbreviation that refers to a mathematical structure that is similar to a ring but does not necessarily require the existence of a multiplicative identity (i.e., an element that acts as 1 in multiplication).

As of my last update in October 2023, "Epigroup" does not refer to a widely recognized term, company, or concept in major fields such as business, technology, or science. It’s possible that it could be a specific brand, organization, or a term used in a niche context that hasn't gained significant recognition or coverage.

In mathematics, the concept of **essential dimension** is a notion in algebraic geometry and representation theory, primarily related to the study of algebraic structures and their invariant properties under field extensions. It provides a way to quantify the "complexity" of objects, such as algebraic varieties or algebraic groups, in terms of the dimensions of the fields needed to define them.

The Finite Lattice Representation Problem is a concept in the field of lattice theory, which deals with partially ordered sets that have specific algebraic properties. In particular, this problem pertains to determining whether a given finite partially ordered set (poset) can be represented as a lattice.

A finitely generated abelian group is a specific type of group in abstract algebra that has some important properties. 1. **Group**: An abelian group is a set equipped with an operation (often called addition) that satisfies four properties: closure, associativity, identity, and inverses. Additionally, an abelian group is commutative, meaning that the order in which you combine elements does not matter (i.e.

A Jónsson–Tarski algebra is a specific type of algebraic structure related to Boolean algebras and described by properties connected to the concept of free algebras. The notion is named after the mathematicians Bjarni Jónsson and Alfred Tarski, who made significant contributions to the fields of mathematical logic and algebra.

A matrix ring is a specific type of ring constructed from matrices over a ring. Formally, if \( R \) is a ring (which can be, for example, a field or another ring), then the set of \( n \times n \) matrices with entries from \( R \) forms a ring, denoted by \( M_n(R) \). The operations defined in this ring are matrix addition and matrix multiplication.

In mathematics, a **module** is a generalization of the concept of a vector space. While vector spaces are defined over a field, modules allow for the scalars to be elements of a more general algebraic structure called a ring.

A **monoid** is an algebraic structure that consists of a set equipped with a binary operation that satisfies two key properties: associativity and identity. More formally, a monoid is defined as a tuple \((M, \cdot, e)\), where: 1. **Set \(M\)**: This is a non-empty set of elements.

As of my last update in October 2023, "Monus" could refer to a few different things depending on the context. It may refer to: 1. **Monus (Currency)**: In some contexts, "Monus" might refer to a digital currency or token. It's essential to check specific cryptocurrency platforms or forums for the most recent developments in digital currencies.

A Moufang polygon is a type of combinatorial structure that generalizes certain properties of projective planes and certain geometric configurations. More specifically, Moufang polygons can be viewed as a particular kind of building in the theory of buildings in geometric group theory, related closely to groups of Lie type and algebraic structures. A Moufang polygon can be defined as a finite, strongly regular combinatorial structure defined with respect to a set of vertices and certain incidence relations among them.

In mathematics, particularly in the context of algebra and number theory, a "near-field" may refer to a structure similar to a field, but with weaker properties. A near-field typically satisfies most properties of a field except for certain requirements, such as the existence of multiplicative inverses for all non-zero elements. However, the concept of "near-field" is not as widely recognized or standardized as fields, rings, or groups.

In abstract algebra, a **semigroup** is a fundamental algebraic structure consisting of a set equipped with an associative binary operation. Formally, a semigroup is defined as follows: 1. **Set**: Let \( S \) be a non-empty set.

A pseudo-ring is a mathematical structure that generalizes some properties of rings but does not satisfy all the axioms that typically define a ring. More formally, a pseudo-ring is a set equipped with two binary operations, usually denoted as addition and multiplication, such that it satisfies certain ring-like properties but may lack others.

The term "Right Group" can refer to different organizations or movements depending on the context, such as political or ideological groups that advocate for conservative or right-leaning policies. However, it is not a widely recognized or specific organization without additional context. If you're referring to a particular group, organization, or movement (e.g.

A **semilattice** is an algebraic structure that is a specific type of partially ordered set (poset).

A **semigroup with involution** is an algebraic structure that combines the properties of a semigroup with the concept of an involution. ### Components of a Semigroup with Involution 1. **Semigroup**: A semigroup is a set \( S \) equipped with a binary operation (let's denote it as \( \cdot \)) that satisfies the associative property.

A **semigroupoid** is an algebraic structure that generalizes the notion of a semigroup to a situation where the elements can be thought of as processes or mappings rather than simple algebraic objects. More formally, a semigroupoid can be defined as a category in which every morphism (or arrow) is invertible, but it has a single object, or it can be thought of as a partially defined operation among elements.