Definitions for algebraic structure
al·ge·bra·ic struc·ture

WiktionaryRate this definition:0.0 / 0 votes

1. algebraic structurenoun

   One or more sets together with a set of operations such that the sets are closed under the operations and are satisfying some axioms.

WikipediaRate this definition:0.0 / 0 votes

1. 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. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called scalar multiplication between elements of the field (called scalars), and elements of the vector space (called vectors). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structures of the same type (homomorphisms). In universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure that is a vector space over a field or a module over a commutative ring. The collection of all structures of a given type (same operations and same laws) is called a variety in universal algebra; this term is also used with a completely different meaning in algebraic geometry, as an abbreviation of algebraic variety. In category theory, the collection of all structures of a given type and homomorphisms between them form a concrete category.

WikidataRate this definition:0.0 / 0 votes

1. Algebraic structure

   In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to an arbitrary set with one or more finitary operations defined on it. Common examples of algebraic structures include groups, rings, fields, and lattices. More complex algebraic structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex structures include vector spaces, modules, and algebras. The properties of specific algebraic structures are studied in the branch known as abstract algebra. The general theory of algebraic structures has been formalized in universal algebra. Category theory is used to study the relationships between two or more classes of algebraic structures, often of different kinds. For example, Galois theory studies the connection between certain fields and groups, algebraic structures of two different kinds. In a slight abuse of notation, the word "structure" can also refer only to the operations on a structure, and not the underlying set itself. For example, a phrase "we have defined a ring structure on the set " means that we have defined ring operations on the set . For another example, the group can be seen as a set that is equipped with an algebraic structure, namely the operation .

How to pronounce algebraic structure?

1. Alex

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   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Australian

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   Neerja

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   Oliver

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How to say algebraic structure in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of algebraic structure in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of algebraic structure in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Algebraic_Structure
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Algebraic_Structure
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=algebraic structure