A note on idempotent semirings
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 Bool...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Beheshti University
2025-01-01
|
| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_104793_c3ad43e48e0ab598d02b1afd64b7dccb.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2345-5853 2345-5861 |