For all your dictionary needs!
Tip. You can look up words, expressions, names, titles...
Header of additive group

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

Click on a title to look inside that book (if available):

Google previewLecture 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...

Google previewApplied 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) .

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 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 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 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 ...

Online dictionaries and encyclopedias with entries for Additive group

Click on a label to prioritize search results according to that topic:

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 ...

Share this page


Go to the pronunciation of Additive group to learn how to say it correctly!

Privacy Policy | Cookies Policy
Keyword Tool | Romanian-English Dictionary