Difference between revisions of "Magma"
From Encyclopedia of Mathematics
(Importing text file) |
(LaTeX) |
||
| Line 1: | Line 1: | ||
| − | A set | + | {{TEX|done}} |
| + | |||
| + | A set $M$ endowed with an everywhere defined [[binary operation]] $m : M \times M \rightarrow M$ on it. No conditions are imposed. In particular, a magma need not be [[Commutativity|commutative]] or [[Associativity|associative]]. Of particular importance is the [[free magma]] on an alphabet (set) $X$. A mapping $f : N \rightarrow M$ of one magma into another is a morphism of magmas if $f(m_N(a,b)) = m_M(f(a),f(b))$ for all $a,b \in N$, i.e., if it respects the binary operations. | ||
Revision as of 18:00, 21 November 2014
A set $M$ endowed with an everywhere defined binary operation $m : M \times M \rightarrow M$ on it. No conditions are imposed. In particular, a magma need not be commutative or associative. Of particular importance is the free magma on an alphabet (set) $X$. A mapping $f : N \rightarrow M$ of one magma into another is a morphism of magmas if $f(m_N(a,b)) = m_M(f(a),f(b))$ for all $a,b \in N$, i.e., if it respects the binary operations.
How to Cite This Entry:
Magma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Magma&oldid=34696
Magma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Magma&oldid=34696
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article