Let R be an associative ring with identity and F a class of R-modules. In this article: we first give a detailed treatment of Cartan-Eilenberg F complexes and extend the basic properties of the class F to the class CE(F). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes, including coherent, Noetherian, von Neumann regular rings, QF rings, semisimple rings, hereditary rings and perfect rings., Xiaorui Zhai, Chunxia Zhang., and Obsahuje seznam literatury
This report describes 7 new species of Drosophila found in the Eastern Arc mountains and on Mount Kilimanjaro in Tanzania: D. baucipyga, D. gata, D. kilimanjarica, D. neogata, D. paragata, D. pilocornuta and D. usambarensis spp.n. Two new species complexes, the megapyga species complex (Sophophora subgenus, melanogaster group, montium subgroup) and the gata species complex (Drosophila subgenus) are introduced. Only one species, D. baucipyga of the montium subgroup, has a geographical range matching the whole Eastern Arc, from the Usambara Mts. in the north-east of Tanzania to Mt. Uzungwa in the south-south west of the country. Five others, including one representative of the dentissima group of the Sophophora subgenus, D. usambarensis, and four representatives of the Drosophila subgenus, D. gata, D. neogata, D. paragata and D. pilocornuta, were found only in the Usambara Mts. Two of these five, D. usambarensis and D. pilocornuta were found only in West-Usambara, while two other related species, D. gata and D. paragata, were found only in East-Usambara. Only the distribution of D. neogata covers the whole of the Usambara mountains. Outside the Eastern Arc, another representative of the dentissima group, D. kilimanjarica, was found only on Mount Kilimanjaro. This new, highly specific, montane fauna of Drosophila further contributes to the unique biological diversity of the Eastern Arc Mts. The biogeographic affinities of the new taxa suggest past connections with the Virunga and Ruwenzori ranges and further west with the Cameroon Volcanic Line. It indicates, in particular, that the Eastern Arc forests have passed through a succession of coalescence and fragmentation events.