Epimorphisms in Varieties of Subidempotent Rresiduated Structures

0538234 - ÚI 2022 RIV CH eng J - Článek v odborném periodiku
Moraschini, Tommaso - Raftery, J.G. - Wannenburg, J. J.
Epimorphisms in Varieties of Subidempotent Rresiduated Structures.
Algebra Universalis. Roč. 82, č. 1 (2021), č. článku 6. ISSN 0002-5240. E-ISSN 1420-8911
Grant CEP: GA MŠMT(CZ) EF17_050/0008361
GRANT EU: European Commission(XE) 689176 - SYSMICS
Institucionální podpora: RVO:67985807
Klíčová slova: Epimorphism * Residuated lattice * Brouwerian algebra * Heyting algebra * De Morgan monoid * Esakia space * Substructural logic * Relevance logic * Beth definability
Obor OECD: Pure mathematics
Impakt faktor: 0.526, rok: 2021
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1007/s00012-020-00694-2

A commutative residuated lattice A is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A-). It is proved here that epimorphisms are surjective in a variety K of such algebras A (with or without involution), provided that each finitely subdirectly irreducible algebra B∈ K has two properties: (1) B is generated by lower bounds of e, and (2) the poset of prime filters of B- has finite depth. Neither (1) nor (2) may be dropped. The proof adapts to the presence of bounds. The result generalizes some recent findings of G. Bezhanishvili and the first two authors concerning epimorphisms in varieties of Brouwerian algebras, Heyting algebras and Sugihara monoids, but its scope also encompasses a range of interesting varieties of De Morgan monoids.
Trvalý link: http://hdl.handle.net/11104/0316060