O-direct union
From Encyclopedia of Mathematics
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of semi-groups with zero
The semi-group obtained from the given family 
of semi-groups with zero, pairwise intersecting at this zero, by specifying on 
the multiplication operation that coincides with the original operation on each semi-group 
and is such that 
for different 
. The 
-direct union is also called the orthogonal sum. A number of types of semi-groups can be described by decomposing them in an 
-direct union of known semi-groups (cf., e.g., Maximal ideal; Minimal ideal; Regular semi-group).
References
| [1] | A.H. Clifford, G.B. Preston, "Algebraic theory of semi-groups" , 2 , Amer. Math. Soc. (1967) |
How to Cite This Entry:
O-direct union. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=O-direct_union&oldid=11404
O-direct union. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=O-direct_union&oldid=11404
This article was adapted from an original article by L.N. Shevrin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article