Difference between revisions of "Multiplicative semi-group"
From Encyclopedia of Mathematics
(unital ring yields monoid) |
(Factorial ring and Gauss semigroup) |
||
| Line 2: | Line 2: | ||
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. | 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]]. | ||
Revision as of 18:17, 3 January 2016
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=37346
Multiplicative semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiplicative_semi-group&oldid=37346
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article