Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...

conclusions the patient underwent surgery applying a midline incision. the left kidney showed a lump pattern embedded in lower pole of the right kidney. left sided nephrectomy was performed while temporary right renal artery was clamped temporarily. histopathological evaluation revealed clear cell carcinoma with severe nuclear atypia (fuhrman grade 4/4). however, local recurrence was not detect...

Let H be a cocommutative weak Hopf algebra and let (B,φB) left H-module algebra. In this paper, for twisted convolution invertible morphism σ:H2→B we define its obstruction θσ as Sweedler 3-cocycle with values in the center of B. We obtain that class vanish third cohomology group HφZ(B)3(H,Z(B)) if, only there exists 2-cocycle α:H2→B such H⊗B can endowed crossed product structure α keeping coho...