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In the context of Wikipedia and other collaborative platforms, "stubs" refer to short articles that provide only a limited amount of information on a particular topic. An "Algebraic geometry stub" specifically pertains to a page related to algebraic geometry that is incomplete, lacking in detail, or requires expansion. Algebraic geometry is a field of mathematics that studies the solutions of systems of algebraic equations and their geometric properties.

In the context of category theory, a "stub" typically refers to a brief or incomplete article or entry about a concept, topic, or theorem within the broader field of category theory. It often indicates that the information provided is minimal and that the article requires expansion or additional detail to fully cover the topic. This can include definitions, examples, applications, and important results related to category theory. Category theory itself is a branch of mathematics that deals with abstract structures and the relationships between them.

In the context of Wikipedia, "Commutative algebra stubs" refers to short articles or entries related to the field of commutative algebra that need expansion or additional detail. A "stub" is generally a brief piece of writing that provides minimal information about a topic, often requiring more comprehensive content to adequately cover the subject. Commutative algebra itself is a branch of mathematics that studies commutative rings and their ideals, with applications in algebraic geometry, number theory, and other areas.

In the context of Wikipedia and other collaborative online encyclopedias, a "stub" refers to a very short article or entry that provides minimal information on a given topic but is intended to be expanded over time. Group theory stubs, therefore, are entries related to group theory—an area of abstract algebra that studies algebraic structures known as groups—that lack sufficient detail, thoroughness, or breadth.

Abel's irreducibility theorem is a result in algebra that concerns the irreducibility of certain polynomials over the field of rational numbers (or more generally, over certain fields).

The Alperin–Brauer–Gorenstein theorem is a result in group theory regarding the structure of finite groups. Specifically, it deals with the existence of groups that have certain properties with respect to their normal subgroups and the actions of their Sylow subgroups.

The Andreotti–Grauert theorem is a result in complex geometry and several complex variables. It addresses the properties of complex spaces and certain types of submanifolds known as complex manifolds. The theorem specifically relates to the existence of holomorphic (complex-analytic) functions on compact complex manifolds.

Aperiodic semigroups are a concept from algebra, specifically within the study of semigroup theory. A semigroup is a set equipped with an associative binary operation. To understand aperiodicity in this context, it's essential to delve into some definitions associated with semigroups.

An Arf semigroup is a specific type of algebraic structure studied in the context of commutative algebra and algebraic geometry, especially in the theory of integral closures of rings and in the classification of singularities.

An **arithmetic ring**, commonly referred to as an **arithmetic system** or simply a **ring**, is a fundamental algebraic structure in the field of abstract algebra. Specifically, a ring is a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication.

The Artin-Zorn theorem is a result in the field of set theory and is often discussed in the context of ordered sets and Zorn's lemma. It specifically deals with the existence of maximal elements in certain partially ordered sets under certain conditions.

Auslander algebra is a concept in representation theory and homological algebra, primarily associated with the study of finitely generated modules over rings. The topic is named after the mathematician Maurice Auslander, who made significant contributions to both representation theory and commutative algebra. At its core, the Auslander algebra of a module category is constructed from the derived category of finitely generated modules over a particular ring.

An automorphism of a Lie algebra is a specific type of isomorphism that is defined within the context of Lie algebras. To be more precise, consider a Lie algebra \( \mathfrak{g} \) over a field (commonly the field of real or complex numbers).

The Baer–Suzuki theorem is a result in group theory that deals with the structure of groups, specifically p-groups, and the conditions under which certain types of normal subgroups can be constructed. The theorem is part of a broader study in the representation of groups and the interplay between their normal subgroups and group actions.

A Brandt semigroup is a specific type of algebraic structure that arises in the context of semigroups, which are sets equipped with an associative binary operation. More formally, a Brandt semigroup is defined as follows: A Brandt semigroup is a semigroup of the form \( B_{n}(G) \) for some positive integer \( n \) and some group \( G \).

The Brauer–Fowler theorem is a result in the field of group theory, more specifically in the study of linear representations of finite groups. It deals with the structure of certain finite groups and their representations over fields with certain characteristics.

The Brauer–Nesbitt theorem is a result in the theory of representations of finite groups, specifically pertaining to the representation theory of the symmetric group. The theorem characterizes the irreducible representations of a symmetric group \( S_n \) in terms of their behavior with respect to certain arithmetic functions.

The Brauer–Suzuki theorem is a result in group theory, specifically in the area of representation theory and the theory of finite groups. Named after mathematicians Richard Brauer and Michio Suzuki, the theorem provides important conditions for the existence of certain types of groups and their representations. One of the most prominent statements of the Brauer–Suzuki theorem pertains to the structure of finite groups, characterizing when a certain kind of simple group can be singly generated by an element of specific order.

The Brauer–Suzuki–Wall theorem is a result in group theory, specifically in the area of representation theory. The theorem deals with the characterization of certain types of groups, known as \( p \)-groups, and their representation over fields of characteristic \( p \).

A CAT(k) group is a type of geometric group that arises in the study of metric spaces and their large-scale geometric properties. The term "CAT(k)" comes from the work of mathematician Mikhail Gromov and relates to CAT(0) spaces, which are simply connected spaces that have non-positive curvature in a very generalized sense. In this context, a **CAT(k)** space is a geodesic metric space that satisfies a condition related to triangles.