We study minimal and almost minimal varieties of commutative integral residuated lattices. In particular, we prove that the variety GBA of generalized Boolean algebras and the variety C generated by the negative integers are the only two semilinear atoms. Furthermore, we give a characterization of all the finitely generated covers of GBA, showing that there are infinitely many, we axiomatize the unique common cover of GBA and C, and we construct continuum-many semilinear covers of C and infinitely many non-semilinear ones.
Agliano, P., Galatos, N., Marcos, M.A. (2024). Almost minimal varieties of commutative residuated lattices. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION [10.1142/S0218196724500309].
Almost minimal varieties of commutative residuated lattices
Agliano, Paolo
;
2024-01-01
Abstract
We study minimal and almost minimal varieties of commutative integral residuated lattices. In particular, we prove that the variety GBA of generalized Boolean algebras and the variety C generated by the negative integers are the only two semilinear atoms. Furthermore, we give a characterization of all the finitely generated covers of GBA, showing that there are infinitely many, we axiomatize the unique common cover of GBA and C, and we construct continuum-many semilinear covers of C and infinitely many non-semilinear ones.
| File | Dimensione | Formato | |
|---|---|---|---|
|
almost minimal AAM.pdf
non disponibili
Tipologia:
Post-print
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
3.42 MB
Formato
Adobe PDF
|
3.42 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/1264994