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Suppose that E D AOExI ; ı is an Ore extension with an automorphism. It is proved that if A is twisted Calabi-Yau of dimension d , then E is twisted Calabi-Yau of dimension d C 1. The relation between their Nakayama automorphisms is also studied. As an application, the Nakayama automorphisms of a class of 5-dimensional Artin-Schelter regular algebras are given explicitly.

Pathogenic fungi including Penicillium digitatum and Penicillium italicum are the main destructive pathogens in the citrus industry, causing great losses during postharvest process. To our knowledge, only one mycovirus from P. digitatum has been reported, and the prevalence of such mycoviruses against citrus postharvest pathogenic fungi and their genotyping were still under investigation. In the present study, we showed that 39 of 152 Penicillium isolates from main citrus-growing areas in China were infected with various mycoviruses belonging to polymycoviruses, Narna-like viruses, and families Totiviridae, Partitivirdae and Chrysoviridae. The next generation sequencing (NGS) towards virus genome library and the following molecular analysis revealed two novel mycoviruses Penicillium digitatum polymycovirus 1 (PdPmV1) and Penicillium digitatum Narna-like virus 1 (PdNLV1), coexisting in P. digitatum strain HS-RH2. The fungicide-resistant P. digitatum strains HS-F6 and HS-E9 coinfected by PdPmV1 and PdNLV1 exhibited obvious reduction in triazole drug prochloraz resistance by mycelial growth analysis on both PDA plates and citrus fruit epidermis with given prochloraz concentration. This report at the first time characterized two novel mycoviruses from P. digitatum and revealed the mycovirus-induced reduction of fungicide resistance.