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## Definition of the noun Additive group

What does Additive group mean as a name of something?

noun

1. [mathematics] An abelian group, when it is written using the symbol '+' for its binary operation
2. [mathematics] The 'underlying group under addition' of a field, ring, vector space or other structure having addition as one of its operations
3. [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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### Lecture Notes on Algebraic Structure of Lattice-Ordered Rings (2014)

by Jingjing Ma

A totally ordered field is a field whose additive group is a totally ordered group and product of two positive elements is still positive. For instance...

### Applied Integer Programming (2011)

Modeling and Solution by Der-San Chen, Robert G. Batson, Yu Dang

An additive group is a group whose operation is an ordinary addition (with modulo 1) .

### 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.

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

by Christopher Clapham, James Nicholson

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

### 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 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 ...

### 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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