Finitely generated commutative, idempotent semirings
- A commutative, idempotent semiring (cisrng) is a semiring in which the
addition is commutative and idempotent. I have two questions:
(1) Is every finitely generated cisrng finitely presented.
(2) Are finitely generated cisrng closed under taking kernel pairs, i.e,
if S is a subsemiring of M an both are finitely generated, then so is
the pullback of the inclusion map from S to M along itself.
I am actually more interested in an answer to (2). Since (2) implies
(1), I am looking for either a counterexample to (1) or for (a reference
to) a proof of (2). I also know that commutative semigroups (or
monoids) are closed under taking kernel pairs; this is in Redei's book
on "The Theory of Finitely Generated Commutative Semigroups".
Dr. Stefan Milius
Institut für Theoretische Informatik Tel: +49 531 391 9524
Technische Universität Braunschweig Fax: +49 531 391 9529
Mühlenpfordtstr. 22-23 s.milius@...
D-38106 Braunschweig http://www.stefan-milius.eu/