additive group
Hello, you have come here looking for the meaning of the word additive group. In DICTIOUS you will not only get to know all the dictionary meanings for the word additive group, but we will also tell you about its etymology, its characteristics and you will know how to say additive group in singular and plural. Everything you need to know about the word additive group you have here. The definition of the word additive group will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofadditive group, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.
English
Noun
additive group (plural additive groups)
- (mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:
- (group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.
- (algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
- (category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.
Usage notes
Borrowing terminology and notation from arithmetic, the additive inverse of an element a is called minus a (denoted −a), and the additive identity is called zero (0).
Translations
group or algebraic object regarded as a group with operation called addition
|