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Difference between revisions of "Multiplicative semi-group"

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(unital ring yields monoid)
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''of an associative ring''
 
''of an associative ring''
  
The [[Semi-group|semi-group]] formed by the elements of the given associative ring relative to multiplication. A non-associative ring is, relative to multiplication, only a [[Groupoid|groupoid]]; it is called the multiplicative groupoid of the ring.
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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.

Revision as of 17:54, 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.

How to Cite This Entry:
Multiplicative semi-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Multiplicative_semi-group&oldid=13440
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article