Epimorphisms in Varieties of Subidempotent Rresiduated Structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00538234" target="_blank" >RIV/67985807:_____/21:00538234 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00012-020-00694-2" target="_blank" >http://dx.doi.org/10.1007/s00012-020-00694-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-020-00694-2" target="_blank" >10.1007/s00012-020-00694-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Epimorphisms in Varieties of Subidempotent Rresiduated Structures

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Epimorphisms in Varieties of Subidempotent Rresiduated Structures

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF17_050%2F0008361" target="_blank" >EF17_050/0008361: Rozvoj lidských zdrojů pro výzkum v teoretické informatice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

1420-8911

Svazek periodika

82

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

26

Strana od-do

6

Kód UT WoS článku

000606863000002

EID výsledku v databázi Scopus

2-s2.0-85098701366