additive group
An "additive group" is a foundational concept in algebra where the operation is defined as addition, playing a crucial role in various mathematical structures such as vector spaces and rings.
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Definition
C1Group Theory
(technical, academic)A set with an addition operation that satisfies associativity, has an identity element, and includes inverses for every element.
Example
- In the group of integers under addition, the number 0 serves as the identity element.
C1Algebra
(technical, academic)A structure where elements can be added, and each element has an additive inverse, forming an abelian group.
Example
- Vector spaces are examples of additive groups where vector addition is the group operation.
C2Category Theory
(technical, academic)A group object in a category where the binary operation is defined as addition.
Example
- Group functors can form additive groups under certain conditions.
Similar
Terms that have similar or relatively close meanings to "additive group":
group theorymain groupuser groupgroup actionfunctional group