### What does **algebraic structure** mean?

# Definitions for algebraic structure

al·ge·bra·ic struc·ture

#### Here are all the possible meanings and translations of the word **algebraic structure**.

### Wiktionary

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.

### Freebase

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 .

### Numerology

Chaldean Numerology

The numerical value of algebraic structure in Chaldean Numerology is:

**2**Pythagorean Numerology

The numerical value of algebraic structure in Pythagorean Numerology is:

**5**

## Translations for **algebraic structure**

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"algebraic structure." *Definitions.net.* STANDS4 LLC, 2022. Web. 27 Sep. 2022. <https://www.definitions.net/definition/algebraic+structure>.

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