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Additive group

Definition of the noun Additive group

What does Additive group mean as a name of something?


  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.


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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Google previewTransactions 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 ...

Google previewThe 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 ...

Google previewThe 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 ...

Google previewTopological 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.

Google previewEncyclopedic 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 ...

Google previewThe Concise Oxford Dictionary of Mathematics (2014)

by Christopher Clapham, James Nicholson

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

Google previewThe 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 ...

Google previewCRC 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 ...

Google previewDictionary 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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