Cotilting modules and homological ring epimorphisms

none1noWe show that every injective homological ring epimorphism f:R--> S where S_R has flat dimension at most one gives rise to a 1-cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and cotilting classes of certain type and in turn, a bijection with a class of smashing localizing subcategories of the derived category of R. Moreover, we obtain that every cotilting class over a valuation domain is a Tor-orthogonal class, hence it is of cocountable type even though in general cotilting classes are not of cofinite type.mixedBazzoni, SilvanaBazzoni, Silvan

Fundamental Labour Rights after the Lisbon Agenda. WP C.S.D.L.E. "Massimo D'Antona" N. 36/2005

[From the Introduction]. This chapter is focused principally on current developments in European social and employment policies. The intention is to consider the original character of EU legal approaches in these fields and to investigate whether, using the notion of fundamental labour rights, there can be a beneficial expansion of this notion by means of a broader circulation of international sources. ‘Circulation’ is a notion grounded on the necessary interrelation – and in some cases the interdependence – of sources generated within different legal systems. A ‘pluralistic’ point of view, not new in Western European legal traditions, reappears in current legal discourse. The main objective of this chapter is to capture developments occurring within national and supranational legal orders, and to interpret their possible outcomes in terms of new entitlements both for individuals and for groups. The hypothesis on which this chapter is based is that the evolution of labour law at national level has been influenced by EU law, while maintaining its own dominant characteristics. This observation suggests that national diversities enrich the multi-cultural and multi-level legal environment in which law-making takes place. In the first phase of the so-called Lisbon strategy, national legislatures have been extremely active in furthering labour law reforms. Legislation adopted over the years has intervened significantly in the regulation of individual contracts of employment and, more broadly, has had an impact on the reform of national labour markets. If one bears in mind the original four pillars of the European employment strategy (EES), one soon realizes that there has been a convergence of national legislatures towards similar areas of intervention. A related argument is that national legislatures had a rather predictable canvas on which lines could be drawn and colours could be mixed

Institutions and local development in Eastern Sicily during the 20th century

In many European countries, economic growth has been characterised by the presence of deep regional imbalances and the Italian case is not an exception. This justifies the adoption of a regional approach in the study of economic development to show the particular path to economic growth, with relation to its own advantages and opportunities on the one hand, and to its own peculiar obstacles and limits on the other hand. In general terms, some particular areas of Eastern Sicily seem to have been benefiting from a relatively dynamic agricultural sector and from its own natural propension to shipping business which have been the stimulus for the development of a modest, but not negligible, group of correlated industries. Since the second half of the 20th century, in these areas, the economic growth engines have been the pharmaceutical, chemical and electronic industries. The main objective of this paper is to analyse the role that local institutions have played in the development of such industries. The answer to this question is complex, but the paper provides some important clues. In particular, it points out the strong co-existence of economic and political interets although mixed in different proportions in each case. This fact confirms that no path to economic growth should be analysed without considering its geographic, economic and political context.

Matlis category equivalences for a ring epimorphism

Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism $u\colon R\to U$. Assuming that the ring epimorphism is homological of flat/projective dimension $1$, we discuss the abelian categories of $u$-comodules and $u$-contramodules and construct the recollement of unbounded derived categories of $R$-modules, $U$-modules, and complexes of $R$-modules with $u$-co/contramodule cohomology. Further assumptions allow to describe the third category in the recollement as the unbounded derived category of the abelian categories of $u$-comodules and $u$-contramodules. For commutative rings, we also prove that any homological epimorphism of projective dimension $1$ is flat. Injectivity of the map $u$ is not required.Comment: LaTeX 2e with tikz-cd, 30 pages, 6 commutative diagrams. v.1: This is an improved, expanded version of Sections 16-18 of the long preprint arXiv:1807.10671v1, which was divided into three parts. v.2: Terminological change of "u-h-divisible" to "u-divisible"; Remark 1.2(1), Proposition 2.4, Lemma 3.4, and Remark 3.5 inserted; references added; v.3: Final versio

Magnetization reversal behavior in complex shaped Co nanowires: a nanomagnet morphology optimization

A systematic micromagnetic study of the morphological characteristic effects over the magnetic static properties of Co-based complex shaped nanowires is presented. The relevance of each characteristic size (i.e. length L, diameter d, and size of the nanowires head T) and their critical values are discussed in the coercive field optimization goal. Our results strongly confirms that once the aspect ratio (L/d) of the nanowire is bigger than around 10, the length is no more the pertinent parameter and instead the internal diameter and the shape of the nanowires play a key role. We attribute this behavior to the non uniform distribution of the demagnetizing field which is localized in the nanowires head and acts as a nucleation point for the incoherent magnetization reversal. Finally, angular dependence of the magnetization are simulated and compared to the case of a prolate spheroid for all considered morphologies.Comment: 7 pages, 6 figure

Smashing localizations of rings of weak global dimension at most one

We show for a ring R of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in R. If, moreover, R is commutative, we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms. We also classify smashing localizations of the derived category of any valuation domain, and provide an easy criterion for the Telescope Conjecture (TC) for any commutative ring of weak global dimension at most one. As a consequence, we show that the TC holds for any commutative von Neumann regular ring R, and it holds precisely for those Pr\"ufer domains which are strongly discrete.Comment: 45 pages; version 2: several changes in the presentation (a section on the homotopy category of dg algebras became an appendix, more explanation added at various places of the text), main results unchange

Early Years Developmental Journal

The Early Years Developmental Journal is based on extensive analysis of a wide range of developmental assessment tools. It is a resource for families and practitioners working closely with them to record a child’s developments to better aid the identification of areas where additional help may be required. It is designed to support key working and foster communication between all those involved in a child’s development. While its primary use is for families, it is also intended that the Journal will be a useful resource for the 24-30 month statutory EYFS progress assessment as well as supporting child health monitoring