Idempotent generated algebras and Boolean powers of commutative rings

A Boolean power S of a commutative ring R has the structure of a commutative R-algebra, and with respect to this structure, each element of S can be written uniquely as an R-linear combination of orthogonal idempotents so that the sum of the idempotents is 1 and their coefficients are distinct. In order to formalize this decomposition property, we introduce the concept of a Specker R-algebra, and we prove that the Boolean powers of R are up to isomorphism precisely the Specker R-algebras. We also show that these algebras are characterized in terms of a functorial construction having roots in the work of Bergman and Rota. When R is indecomposable, we prove that S is a Specker R-algebra iff S is a projective R-module, thus strengthening a theorem of Bergman, and when R is a domain, we show that S is a Specker R-algebra iff S is a torsion-free R-module. For an indecomposable R, we prove that the category of Specker R-algebras is equivalent to the category of Boolean algebras, and hence is dually equivalent to the category of Stone spaces. In addition, when R is a domain, we show that the category of Baer Specker R-algebras is equivalent to the category of complete Boolean algebras, and hence is dually equivalent to the category of extremally disconnected compact Hausdorff spaces. For a totally ordered R, we prove that there is a unique partial order on a Specker R-algebra S for which it is an f-algebra over R, and show that S is equivalent to the R-algebra of piecewise constant continuous functions from a Stone space X to R equipped with the interval topology.Comment: 18 page

De Vries powers: a generalization of Boolean powers for compact Hausdorff spaces

We generalize the Boolean power construction to the setting of compact Hausdorff spaces. This is done by replacing Boolean algebras with de Vries algebras (complete Boolean algebras enriched with proximity) and Stone duality with de Vries duality. For a compact Hausdorff space $X$ and a totally ordered algebra $A$, we introduce the concept of a finitely valued normal function $f:X\to A$. We show that the operations of $A$ lift to the set $FN(X,A)$ of all finitely valued normal functions, and that there is a canonical proximity relation $\prec$ on $FN(X,A)$. This gives rise to the de Vries power construction, which when restricted to Stone spaces, yields the Boolean power construction. We prove that de Vries powers of a totally ordered integral domain $A$ are axiomatized as proximity Baer Specker $A$-algebras, those pairs $(S,\prec)$, where $S$ is a torsion-free $A$-algebra generated by its idempotents that is a Baer ring, and $\prec$ is a proximity relation on $S$. We introduce the category of proximity Baer Specker $A$-algebras and proximity morphisms between them, and prove that this category is dually equivalent to the category of compact Hausdorff spaces and continuous maps. This provides an analogue of de Vries duality for proximity Baer Specker $A$-algebras.Comment: 34 page

Profinite completions and canonical extensions of Heyting algebras

We show that the profinite completions and canonical extensions of bounded distributive lattices and of Boolean algebras coincide. We characterize dual spaces of canonical extensions of bounded distributive lattices and of Heyting algebras in terms of Nachbin order-compactifications. We give the dual description of the profinite completion H of a Heyting algebra H, and characterize the dual space of H. We also give a necessary and sufficient condition for the profinite completion of H to coincide with its canonical extension, and provide a new criterion for a variety V of Heyting algebras to be finitely generated by showing that V is finitely generated if and only if the profinite completion of every member of V coincides with its canonical extension. From this we obtain a new proof of a well-known theorem that every finitely generated variety of Heyting algebras is canonical

Up-regulation of a death receptor renders antiviral T cells susceptible to NK cell-mediated deletion

This article is distributed under the terms of an Attribution–Noncommercial–Share Alike–No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms). After six months it is available under a Creative Commons License (Attribution–Noncommercial–Share Alike 3.0 Unported license, as described at http://creativecommons.org/licenses/by-nc-sa/3.0/).This work was funded by the Medical Research Council (Clinical Research Training Fellowship to DP and grant G0801213 to M.K. Maini)

Pantropical modelling of canopy functional traits using Sentinel-2 remote sensing data

Funding Information: This work is a product of the Global Ecosystems Monitoring (GEM) network (gem.tropicalforests.ox.ac.uk). J.A.G. was funded by the Natural Environment Research Council (NERC; NE/T011084/1 and NE/S011811/1) and the Netherlands Organisation for Scientific Research (NWO) under the Rubicon programme with project number 019.162LW.010. The traits field campaign was funded by a grant to Y.M. from the European Research Council (Advanced Grant GEM-TRAIT: 321131) under the European Union‘s Seventh Framework Programme (FP7/2007-2013), with additional support from NERC Grant NE/D014174/1 and NE/J022616/1 for traits work in Peru, NERC Grant ECOFOR (NE/K016385/1) for traits work in Santarem, NERC Grant BALI (NE/K016369/1) for plot and traits work in Malaysia and ERC Advanced Grant T-FORCES (291585) to Phillips for traits work in Australia. Plot setup in Ghana and Gabon were funded by a NERC Grant NE/I014705/1 and by the Royal Society-Leverhulme Africa Capacity Building Programme. The Malaysia campaign was also funded by NERC GrantNE/K016253/1. Plot inventories in Peru were supported by funding from the US National Science Foundation Long-Term Research in Environmental Biology program (LTREB; DEB 1754647) and the Gordon and Betty Moore Foundation Andes-Amazon Program. Plots inventories in Nova Xavantina (Brazil) were supported by the National Council for Scientific and Technological Development (CNPq), Long Term Ecological Research Program (PELD), Proc. 441244/2016-5, and the Foundation of Research Support of Mato Grosso (FAPEMAT), Project ReFlor, Proc. 589267/2016. During data collection, I.O. was supported by a Marie Curie Fellowship (FP7-PEOPLE-2012-IEF-327990). GEM trait data in Gabon was collected under authorisation to Y.M. and supported by the Gabon National Parks Agency. D.B. was funded by the Fondation Wiener-Anspach. W.D.K. acknowledges support from the Faculty Research Cluster ‘Global Ecology’ of the University of Amsterdam. M.S. was funded by a grant from the Ministry of Education, Youth and Sports of the Czech Republic (INTER-TRANSFER LTT19018). Y.M. is supported by the Jackson Foundation. We thank the two anonymous reviewers and Associate Editor G. Henebry for their insightful comments that helped improved this manuscript.Peer reviewedPostprin

Eunotiaceae (Bacillariophyceae) em igarapés da Amazônia Central, Manaus e Presidente Figueiredo, Brasil

Estudos florísticos e taxonômicos envolvendo diatomáceas são escassos para a região amazônica. As publicações existentes incluem registros de diatomáceas da Amazônia brasileira, do Equador, da Colômbia e do Peru e comumente mostram que Eunotia e Actinella (Eunotiaceae) são gêneros bem representados nessa região. A maioria dos igarapés amazônicos costuma apresentar potencial hidrogeniônico (pH) ácido, característica aquática que promove o desenvolvimento de uma comunidade típica de diatomáceas, dominada por espécimes de Eunotiaceae. O objetivo deste trabalho foi providenciar um levantamento florístico das espécies de Eunotiaceae presentes em igarapés da Amazônia Central brasileira e registrar os morfotipos de algumas espécies. Amostras fitoplanctônicas e perifíticas foram coletadas em cinco igarapés na rodovia BR-174, em Manaus e Presidente Figueiredo, em setembro e outubro de 1996 e fevereiro e março de 1997. Lâminas permanentes foram preparadas de acordo com a técnica de oxidação lenta para o estudo qualitativo. Vinte e três espécies pertencentes ao gênero Eunotia e seis ao gênero Actinella foram determinadas. Chaves dicotômicas de identificação, descrição detalhada, comentários relevantes e ilustrações foram providenciadas para cada táxon determinado. Morfotipos foram documentados para Eunotia zygodon. Espécies raramente citadas na literatura foram registradas, tais como, Eunotia falcifera e Eunotia rostellata.Floristic and taxonomical studies about diatoms to Amazonian region are commonly well represented by Eunotia and Actinella (Eunotiaceae). The available works include diatom assemblage from Brazilian, Ecuadorian, Colombian and Peruvian Amazonia. The local streams often present acid pH which provides environmental conditions to develop a very particular diatom community dominated by specimens of Eunotiaceae. Thus, the aim of this paper is to give a floristic survey of Eunotiaceae from central Amazonian rivers and to register the typical morphologic frustule variations of some species. Planktonic and periphytic samples were collected from five rivers located at the BR-174 highway, near Manaus and Presidente Figueiredo districts, during 1996 and 1997. Slides were prepared in accordance with the technique of slow oxidation for the qualitative determination. Twenty-three species of Eunotia and six of Actinella were identified. Dicotomic keys, taxonomic comments and photographic illustrations were added. Morphotypes of Eunotia zygodon were registered. Species scarcelly mentioned on diatom literature were registered, such as, Eunotia falcifera and Eunotia rostellata