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Congruence-simple semirings
by
Tomas Kepka
The Charles Univerzity, Praha, Czech Republic
A semiring is an algebra with two associative binary operations, an addition and a multiplication, such that the addition is commutative and the multiplication distributes over the addition. A semiring is said to be congruence-simple if it possesses exatly two congruence relations. Now, if S is such a semiring, then just one of the following five cases takes place:
(1) |S| = 2; (2) |S| >= 3 and x+x=x; (3) |S| >= 3 and x+y=x+z implies y=z; (4) |S| >= 3, x+x=o, S+o=o and S+S=S; (5) |S| >= 3, S+S=o and SS=S.
Date received: May 18, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-37.