# Additive group

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## Definition of the noun Additive group

What does Additive group mean as a name of something?

**noun**

- [
*mathematics*] An abelian group, when it is written using the symbol '+' for its binary operation - [
*mathematics*] The 'underlying group under addition' of a field, ring, vector space or other structure having addition as one of its operations - [
*mathematics*] A group scheme representing the underlying-additive-group functor.

## Explanation

**Additive group**: An additive group is a group of which the group operation is to be thought of as addition in some sense. It is usually abelian, and typically written using the symbol + for its binary operation.

## Printed dictionaries and other books with definitions for Additive group

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### Transactions of the American Mathematical Society (1905)

Since * the additive group is an abelian group of type* (
1,1, • □ •, 1 ), its group of isomorphisms is the general linear homogeneous ...

### The Theory of Infinite Soluble Groups (2004)

by John C. Lennox, Derek J. S. Robinson

Let R be an integral domain whose
* additive group is a torsion-free minimax group*. Then the group of units ofR is ...

### The Concise Handbook of Algebra (2002)

by Aleksandr Vasilʹevich Mikhalev, Günter Pilz

a ring with identity
whose * additive group is a free abelian group of a finite rank n with Z-basis e*\, . . . ,
en. Every Z- ring A is naturally embedded in a Q-algebra A = A 0Z Q with ...

### Topological Rings Satisfying Compactness Conditions (2012)

by M. Ursul

The Jacobson radical of a locally compact ring with
almost connected * additive group is an inverse limit of nilpotent rings*. PROOF.

### Encyclopedic Dictionary of Mathematics (1993)

by Kiyosi Itô

Torsion-Free Groups In Abelian groups, the group operation is
often written a+b, using the additive notation; an additiver written group, called **an
additive group**, is generally assumed to be Abelian. In the rest of this article we ...

### The Concise Oxford Dictionary of Mathematics (2014)

by Christopher Clapham, James Nicholson

**additive group** A *group with the
operationþ, called ...

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

**additive group** A *group for which the result of
combining a and b is written as a + b, and the group identity is denoted by 0. In a
*ring the term is often used to refer to the group obtained by considering all the ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

For example, **the additive group** of whole numbers is free with a single generator,
1. See also FREE ABELIAN GROUP, FREE SEMIGROUP Free Semigroup A
SEMIGROUP with a noncommutative product in which no PRODUCT can ever be
...

### Dictionary of Distances (2006)

by Michel-Marie Deza, Elena Deza

**additive group** K, given by the logarithm of the valuation. Every other proper
continuous homomorphism v' : T — > W is of the form v' = a □ v with a e GL(n, K).
If ||.|| is a norm on W, one obtains the corresponding semi-norm \\x\\T=\\v(x)\\onT.

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## Video about Additive group

**Additive group Meaning**

Video shows what additive group means. An abelian group, when it is written using the symbol + for its binary operation. The underlying group under addition of ...

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