Abstract
A ring A is a set, together with two laws of composition called multiplication and addition respectively, and written as a product and as a sum respectively, satisfying the following conditions:
-
RI 1.
With respect to addition, A is a commutative group.
-
RI 2.
The multiplication is associative, and has a unit element.
-
RI 3.
For all x, y, z ∈ A we have
$$ (x + y)z = xz + yz and z(x + y) = zx + zy. $$
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lang, S. (2002). Rings. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0041-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6551-1
Online ISBN: 978-1-4613-0041-0
eBook Packages: Springer Book Archive