A ring R is (weakly) nil clean provided that every element in R is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let R be abelian, and let n 2 N. We prove that Mn(R) is nil clean if and only if R/J(R) is Boolean and Mn(J(R)) is nil. Furthermore, we prove that R is weakly nil clean if and only if R is periodic; R/J(R) is Z3, B or Z3 B where B is a Boolean ring, and that Mn(R) is weakly nil clean if and only if Mn(R) is nil clean for all n > 2., Nahid Ashrafi, Marjan Sheibani, Huanyin Chen., and Seznam literatury
Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.
This study introduces an emblematic scheme within the stucco decoration of the Palace Chapel in Červené Poříčí. The given emblematic sheme glorifies the Most Sacred Heart of Jesus. It was inspired by the emblem book of the Bavarian theologian Anton Ginther, which was published in 1706. The article tries to place the programme of the decoration into the context of Middle European evolution of the devotion to the Most Sacred Heart of Jesus - a cult that was very popular at the time. Finally, the article places the decorative scheme into political and historical context and discusses the role its patron played in determining the decoration’s commission and execution., Daniela Štěrbová., and Obsahuje bibliografické odkazy