Academic literature on the topic 'Grading'

We describe all group gradings of the matrix algebra M2(k), where k is an arbitrary field. We prove that any such grading reduces to a grading of type C2, a grading of type C2 × C2, or to a good grading. We give new simple proofs for the description of C2-gradings and C2 × C2-gradings on M2(K).

In the study of the structure of graded algebras (such as graded ideals, graded subspaces, and radicals) or graded polynomial identities, the grading group can be replaced by any other group that realizes the same grading. Here we come to the notion of weak equivalence of gradings: two gradings are weakly equivalent if there exists an isomorphism between the graded algebras that maps each graded component onto a graded component. Each group grading on an algebra can be weakly equivalent to G-gradings for many different groups G; however, it turns out that there is one distinguished group among them, called the universal group of the grading. In this paper we study categories and functors related to the notion of weak equivalence of gradings. In particular, we introduce an oplax 2-functor that assigns to each grading its support, and show that the universal grading group functor has neither left nor right adjoint.

10059 Background: Soft tissue sarcomas (STS) are rare, mesenchymal derived tumors. Based on malignancy, three grades are distinguished with G1 equaling low grade, G2 intermediate grade and G3 high grade, respectively. Studies have shown that some G1 tumors which underwent complete surgical resection reoccurred as lesions with a grading shift from G1 to higher malignancy. This grading change is referred to as up grading. Patients with grading changes were thoroughly examined in our study. Our aim was to find possible risk factors for up gradings, such as age, localization of tumor and tumor type. Methods: This retrospective case control study evaluated 333 Patients, who, between 1996 to 2011 were treated for G1 STS at Bergmannsheil Bochum, university clinic. These patients received complete initial surgical resection. Among our 333 patients, 9.9% (n=33) developed up gradings of their STS. These were then reviewed more closely in the aim of finding possible risk factors. We did not exclude any patients from our data or deliberately pick any grading changers and regard our collective as randomly sampled. The processed data includes age, gender, tumor type, tumor localization, occurrence of recidive and grading change. Results: Patients with up gradings were found to have a higher mean age of 4, 5 years than reference collective. The tumor type has a strong, statistically significant effect on grading change as patients with fibrosarcomas have a threefold risk of developing up gradings when compared to patients with other G1 STS. Conclusions: Our results indicate that age and tumor type play the key role in the development of up gradings in low malignant STS .Patients aged 60 and above diagnosed with fibrosarcomas are at a 3 times higher risk of developing a grading change as opposed to patients younger than 60 with other low grade STS than fibrosarcoma. We discussed the significance of these risk factors and argued whether, in addition to wide tumor resection, a short term postoperative radiotherapy should be applied for these patients to improve therapeutical outcome.

Zusammenfassung Hintergrund Im Jahr 2014 wurde durch die ISUP (International Society of Urological Pathology) eine Modifikation des Gradings für das Prostatakarzinom (PCa) eingeführt, welches 2016 von der Weltgesundheitsorganisation (WHO) anerkannt und übernommen wurde. Neben der Definition von 5 „Grade Groups“ wurden auch einige histomorphologische Kriterien angepasst. Unsere Übersichtsarbeit stellt die Ergebnisse aller aktuellen Studien und deren Bewertungen des neuen Gradings zusammen. Material und Methoden Es erfolgte eine Literaturrecherche in der PubMed-Datenbank. Insgesamt sind aus dem Zeitraum 2016 – 2018 15 Studien identifiziert und in die Übersicht eingeschlossen worden. Ergebnisse Die Hauptziele des neuen ISUP 2014/WHO 2016 PCa-Gradings sind ein (I) präziseres und vereinfachtes Grading, (II) eine verringerte Übertherapie indolenter PCa und (III) eine verbesserte Kommunikation mit den Patienten. Die Mehrzahl der Studien wählte das biochemische Rezidiv als Endpunkt und bescheinigte dem neuen Grading eine höhere prognostische Wertigkeit im Vergleich zum früheren Gleason Grading. Interessanterweise war es jedoch nur in wenigen Studien klar ersichtlich, dass die archivierten Proben tatsächlich auch nach den modifizierten histomorphologischen Kriterien reevaluiert („Re-Grading“) und nicht nur in die neuen „Grade Groups“ übersetzt wurden („Re-Grouping“). Schlussfolgerung Die Mehrheit der analysierten Studien bestätigt die prognostische Wertigkeit des neuen ISUP 2014/WHO 2016 Gradings und empfiehlt dessen weltweite Anwendung. Jedoch muss bei der Interpretation bisheriger Studien berücksichtigt werden, dass das notwendige „Re-Grading“ als korrekte Anwendung des neuen Gradings nicht immer klar ersichtlich war.