A note on idempotent semirings
نویسندگان
1 Department of Mathematics, Faculty of Science and Technology, University of Coimbra, Portugal.
2 Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa.
doi
10.48308/cgasa.2024.235337.1484چکیده
For a commutative semiring $S$, by an $S$-algebra we mean a commutative semiring $A$ equipped with a homomorphism $S\to A$. We show that the subvariety of $S$-algebras determined by the identities $1+2x=1$ and $x^2=x$ is closed under non-empty colimits. The (known) closedness of the category of Boolean rings and of the category of distributive lattices under non-empty colimits in the category of commutative semirings both follow from this general statement.
