Namespaces
Variants
Actions

Multiplicative semi-group

From Encyclopedia of Mathematics
Revision as of 18:18, 3 January 2016 by Richard Pinch (talk | contribs) (TeX done)
Jump to: navigation, search

of an associative ring

The semi-group formed by the elements of the given associative ring relative to multiplication. In a unital ring (ring with multiplicative identity) this is a monoid. A non-associative ring is, relative to multiplication, only a magma; it is called the multiplicative system of the ring.

Some properties of a ring can be expressed in terms of the multiplicative semigroup. For example, a factorial ring is one with a multiplicative Gauss semi-group.

How to Cite This Entry:
Multiplicative semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiplicative_semi-group&oldid=37347
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article