An alternative perspective on projectivity of modules

Similar to the idea of relative projectivity, we introduce the notion of relative subprojectivity, which is an alternative way to measure the projectivity of a module. Given modules $M$ and $N$, $M$ is said to be {\em $N$-subprojective} if for every epimorphism $g:B \rightarrow N$ and homomorphism $f:M \rightarrow N$, then there exists a homomorphism $h:M \rightarrow B$ such that $gh=f$. For a module $M$, the {\em subprojectivity domain of $M$} is defined to be the collection of all modules $N$ such that $M$ is $N$-subprojective. A module is projective if and only if its subprojectivity domain consists of all modules. Opposite to this idea, a module $M$ is said to be {\em subprojectively poor}, or {\em $sp$-poor} if its subprojectivity domain is as small as conceivably possible, that is, consisting of exactly the projective modules. Properties of subprojectivity domains and $sp$-poor modules are studied. In particular, the existence of an $sp$-poor module is attained for artinian serial rings.Comment: Dedicated to the memory of Francisco Raggi; v2 some editorial changes. 'Right hereditary right perfect' replaced by the (equivalent) condition 'right hereditary semiprimary'; v3 a mistake corrected in the statements of Propositions 3.8 and 3.

Fauna Europaea: Diptera -Brachycera

Link to publication Citation for published version (APA): Pape, T., Beuk, P., Pont, A. C., Shatalkin, A. I., Ozerov, A. L., Woźnica, A. J., ... de Jong, Y. (2015). Fauna Europaea: 3, [e4187]. https://doi.org/10.3897/BDJ.3.e4187 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Abstract Fauna Europaea provides a public web-service with an index of scientific names (including important synonyms) of all extant multicellular European terrestrial and freshwater animals and their geographical distribution at the level of countries and major islands (east of the Urals and excluding the Caucasus region). The Fauna Europaea project comprises about 230,000 taxonomic names, including 130,000 accepted species and 14,000 accepted subspecies, which is much more than the originally projected number of 100,000 species. Fauna Europaea represents a huge effort by more than 400 contributing taxonomic specialists throughout Europe and is a unique (standard) reference suitable for many user communities in science, government, industry, nature conservation and education. The Diptera-Brachycera is one of the 58 Fauna Europaea major taxonomic groups, and data have been compiled by a network of 55 specialists. Within the two-winged insects (Diptera), the Brachycera constitute a monophyletic group, which is generally given rank of suborder. The Brachycera may be classified into the probably paraphyletic 'lower brachyceran grade' and the monophyletic Eremoneura. The latter contains the Empidoidea, the Apystomyioidea with a single Nearctic species, and the Cyclorrhapha, which in turn is divided into the paraphyletic 'aschizan grade' and the monophyletic Schizophora. The latter is traditionally divided into the paraphyletic 'acalyptrate grade' and the monophyletic Calyptratae. Our knowledge of the European fauna of Diptera-Brachycera varies tremendously among families, from the reasonably well known hoverflies (Syrphidae) to the extremely poorly known scuttle flies (Phoridae). There has been a steady growth in our knowledge of European Diptera for the last two centuries, with no apparent slow down, but there is a shift towards a larger fraction of the new species being found among the families of the nematoceran grade (lower Diptera), which due to a larger number of small-sized species may be considered as taxonomically more challenging. Most of Europe is highly industrialised and has a high human population density, and the more fertile habitats are extensively cultivated. This has undoubtedly increased the extinction risk for numerous species of brachyceran flies, yet with the recent re-discovery of Thyreophora cynophila (Panzer), there are no known cases of extinction at a European level. However, few national Red Lists have extensive information on Diptera. For the Diptera-Brachycera, data from 96 families containing 11,751 species are included in this paper

RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN

A Paraître Glasgow Mathematical JournalR is called a right WV -ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV -ring, then R is right uniform or a right V -ring. It is shown that for a right WV-ring R, R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS or noetherian module. For a finitely generated module M with projective socle over a V -ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X \oplus T, where X is semisimple and T is noetherian with zero socle. In the case that M = R, we get R = S \oplus T, where S is a semisimple artinian ring, and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian

Fauna Europaea: Diptera – Brachycera: Fauna Europaea: Diptera – Brachycera

Fauna Europaea provides a public web-service with an index of scientific names (including important synonyms) of all extant multicellular European terrestrial and freshwater animals and their geographical distribution at the level of countries and major islands (east of the Urals and excluding the Caucasus region). The Fauna Europaea project comprises about 230,000 taxonomic names, including 130,000 accepted species and 14,000 accepted subspecies, which is much more than the originally projected number of 100,000 species. Fauna Europaea represents a huge effort by more than 400 contributing taxonomic specialists throughout Europe and is a unique (standard) reference suitable for many user communities in science, government, industry, nature conservation and education. The Diptera–Brachycera is one of the 58 Fauna Europaea major taxonomic groups, and data have been compiled by a network of 55 specialists.Within the two-winged insects (Diptera), the Brachycera constitute a monophyletic group, which is generally given rank of suborder. The Brachycera may be classified into the probably paraphyletic 'lower brachyceran grade' and the monophyletic Eremoneura. The latter contains the Empidoidea, the Apystomyioidea with a single Nearctic species, and the Cyclorrhapha, which in turn is divided into the paraphyletic 'aschizan grade' and the monophyletic Schizophora. The latter is traditionally divided into the paraphyletic 'acalyptrate grade' and the monophyletic Calyptratae. Our knowledge of the European fauna of Diptera–Brachycera varies tremendously among families, from the reasonably well known hoverflies (Syrphidae) to the extremely poorly known scuttle flies (Phoridae). There has been a steady growth in our knowledge of European Diptera for the last two centuries, with no apparent slow down, but there is a shift towards a larger fraction of the new species being found among the families of the nematoceran grade (lower Diptera), which due to a larger number of small-sized species may be considered as taxonomically more challenging.Most of Europe is highly industrialised and has a high human population density, and the more fertile habitats are extensively cultivated. This has undoubtedly increased the extinction risk for numerous species of brachyceran flies, yet with the recent re-discovery of Thyreophora cynophila (Panzer), there are no known cases of extinction at a European level. However, few national Red Lists have extensive information on Diptera.For the Diptera–Brachycera, data from 96 families containing 11,751 species are included in this paper