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Canonical extensions of lattices are more than perfect
Názov Canonical extensions of lattices are more than perfect Aut.údaje Andrew P. K. Craig, Maria J. Gouveia, Miroslav Haviar Autor Craig Andrew, P. K. (34%)
Spoluautori Gouveia Maria Joao (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Zdroj.dok. Algebra Universalis. Vol. 83, no. 2 (2022), pp. [1-17]. - Basel : Springer Nature Switzerland AG, 2022 Kľúč.slová kanonické rozšírenia matematika - mathematics Form.deskr. články - journal articles Jazyk dok. angličtina Krajina Švajčiarsko Anotácia In a paper published in 2015, we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical exten sions of lattices. Here, we firstly introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames into a full categorical framework. We then answer Problem 2 from our 2015 paper by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are ‘more’ than just perfect lattices. We illustrate the correspondences between classes of our newly-described PTi lattices and classes of TiRS graphs by examples. We conclude by outlining a direction for future research. URL Link na plný text Kategória publikačnej činnosti ADC Číslo archívnej kópie 51538 Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika 
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Počet záznamov: 1