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Quasi-hereditary algebras are an important class of algebras with many appli-cations in representation theory, most notably the representation theory of semi-simple complex Lie-algebras. Such algebras sometimes admit an exact Borel sub-algebra, that is a subalgebra satisfying similar formal properties to the Borel sub-algebras from Lie theory. This thesis is divided into two parts. In the first part we classify quasi-hereditary algebras with two simple modules over perfect fields up to Morita equivalence, generalizing a similar result by Membrillo-Hernandez for thealgebraically closed case. In the second part, we take a poset X, a certain set M of constants, and a finite set ρ of paths in the Hasse-diagram of X and construct analgebra A(X, M, ρ) that generalizes the twisted double incidence algebras originally introduced by Deng and Xi. We provide necessary and sufficient conditions for this algebra to be quasi-hereditary when X is a tree, and we show that A(X, M, ρ) admits an exact Borel subalgebra when these conditions are satisfied. Following this, we compute the Ext-algebra of the standard modules of A(X, M, ρ).

Syfte: Att granska hur väl indikatorbilden och rotfyllningsbilden överensstämmer utifrån mätningar med elektronisk apexlokalisator. Dessutom granskas om rotfyllningskvalitet är beroende av tandtyp och antal besök samt om det förekommer någon skillnad på behandlingsproceduren före eller under COVID-19 pandemin. Vidare granskas tecken på läkning i de fall där läkningsbild finns.  Material och metod: Totalt har 635 patienter fått endodontisk behandling på studentklinik för endodonti på Malmö Tandvårdshögskola under perioden 2016–2021. Av dessa uppfyllde 350 journaler inklusionskriterierna. Journaldata tillsammans med röntgenbilder granskades av två oberoende observatörer. Resultat: Av 350 tänder överensstämde 262 tänders indikatorbild och rotfyllningsbild med EAL-mätningar. Underkäksmolarer till följd av överkäksmolarer och överkäkpresmolarer som hade inadekvat rotfyllningskvalitet.  Cirka 70% av tänderna som behandlades färdigt krävde mellan 2–6 besök. Tecken på läkning kunde observeras hos 78 patienter (ca. 92 %) som följts med klinisk undersökning och läkningsbilder. Inga märkbara skillnader noterades i behandlingsproceduren före eller under Covid-19 pandemin. Slutsats: Rotfyllningarna uppvisade god kvalitet baserat på kliniskt och röntgenologiskt underlag. Studenterna behöver relativt många besök för att genomföra en endodontisk behandling. Behandlingen resulterar ofta i en rotfyllning som bedöms ha god kvalitet och så många fall läker. Det behövs ges tydligare rekommendationer till studenter gällande bestämning av arbetslängden och information om att EAL är mer pålitlig att fastställa arbetslängd. / Aim: To evaluate how well the working length radiograph and obturation radiograph corresponded with the working length (WL) measured initially by electronic apex locator (EAL). Furthermore, the aim of this study was to evaluate if the quality of root canal fillings was dependent on tooth type, number of dental visits and if there was any different in treatment procedure before and during the Covid-19 pandemic. Additionally, signs of healing were evaluated if radiographs were available.  Material and method: Patient journal and intraoral radiographs of 635 patients who had undergone endodontic treatment by students at the Faculty of Odontology at University of Malmö during 2016–2021 were evaluated. A total number of 350 patients fulfilled the inclusion’s criteria. Patient’s journal and radiographs were reviewed by two independent observers.  Results: Of 350 teeth, in 262 teeth working length radiograph and obturation radiograph was consistent with the working length determined by EAL. Mandibular morals followed by maxillary molars and premolars were tooth types that failed to keep WL measured by EAL. Approximately 70% teeth were treated between 2-6 visits. In 84 cases radiographs were available and signs of healing were observed in 78 cases (approx. 92%). No significant differences were observed in treatment procedure before and under the Covid-19 pandemic.   Conclusion: The root canal fillings were of good quality based on clinical and radiographic evidence. Students need more time to carry out endodontic treatment but, in most cases, root canal fillings were of good quality and periapical healing was obtained. Furthermore, the students need clearer recommendations regarding determination of WL.