The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Cech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.

In spite of the vast literature on modality in English, very little research has been done on modal adverbs as a group. While there are studies of individual adverbs, the semantic and pragmatic relations between them have been left largely unexplored. This book takes a close look at the whole field of modal certainty as expressed by adverbs in English. On the basis of corpus data the most frequent adverbs of certainty, including certainly, indeed, and no doubt, are examined from the point of view of their syntactic, semantic and pragmatic characteristics. The corpus used is the International Corpus of English - Great Britain, supplemented by data from other present-day English corpora, and questionnaires testing native speakers' intuitions on fine-grained similarities and differences between closely related adverbs. The methodology also includes the study of cross-linguistic equivalents as indicators of semantic-pragmatic relations between adverbs. Translation corpora yield correspondences in Swedish, Dutch, French and German. A detailed study of those correspondences adds useful information for setting up a semantic-pragmatic profile of each adverb, showing where their meanings overlap and where the boundaries are. The concept of semantic maps is relied on for plotting these relations. The book not only provides a thorough empirical study of English adverbs expressing certainty, it also contributes to a better theoretical understanding of the complexity of modal certainty, how it is related to speakers' goals and to other semantic areas. It is the first in-depth study of this kind, combining rich information on English as well as opening up perspectives for further empirical and theoretical research into modality.

This book focuses on how to address persistent linguistically structured inequalities in education, primarily in relation to South African schools, but also in conversation with Australian work and with resonances for other multilingual contexts around the world. The book as a whole lays bare the tension between the commitment to multilingualism enshrined in the South African Constitution and language-in-education policy, and the realities of the dominance of English and the virtual absence of indigenous African languages in current educational practices. It suggests that dynamic plurilingual pedagogies can be allied with the explicit scaffolding of genre-based pedagogies to help redress asymmetries in epistemic access and to re-imagine policies, pedagogies, and practices more in tune with the realities of multilingual classrooms. The contributions to this book offer complementary insights on routes to improving access to school knowledge, especially for learners whose home language or language variety is different to that of teaching and learning at school. All subscribe to similar ideologies which include the view that multilingualism should be seen as a resource rather than a 'problem' in education. Commentaries on these chapters highlight evidence-based high-impact educational responses, and suggest that translanguaging and genre may well offer opportunities for students to expand their linguistic repertoires and to bridge epistemological differences between community and school. This book was originally published as a special issue of Language and Education.

This book focuses on how to address persistent linguistically structured inequalities in education, primarily in relation to South African schools, but also in conversation with Australian work and with resonances for other multilingual contexts around the world. The book as a whole lays bare the tension between the commitment to multilingualism enshrined in the South African Constitution and language-in-education policy, and the realities of the dominance of English and the virtual absence of indigenous African languages in current educational practices. It suggests that dynamic plurilingual pedagogies can be allied with the explicit scaffolding of genre-based pedagogies to help redress asymmetries in epistemic access and to re-imagine policies, pedagogies, and practices more in tune with the realities of multilingual classrooms. The contributions to this book offer complementary insights on routes to improving access to school knowledge, especially for learners whose home language or language variety is different to that of teaching and learning at school. All subscribe to similar ideologies which include the view that multilingualism should be seen as a resource rather than a 'problem' in education. Commentaries on these chapters highlight evidence-based high-impact educational responses, and suggest that translanguaging and genre may well offer opportunities for students to expand their linguistic repertoires and to bridge epistemological differences between community and school. This book was originally published as a special issue of Language and Education.

The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Cech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.

They agreed on one thing before retiring-they would travel, sniff around at other countries and other lifestyles, and discover along the way which place came closest to "having it all." There they would drop anchor and go with the flow. The going has been good, so much so that these former Washingtonians have decided to make France their permanent home. They chose the city over the countryside and took on the challenges and pleasures of Aix-en-Provence, where they have been doing as the locals do for more than a decade now. The daily markets, strikes, gypsies, curious villagers, ancient traditions, truffle cheaters, pagan and religious celebrations, secret swimming spots in the middle of Marseilles-it's all there to be suffered and enjoyed. Not to mention an interest in food that borders on the obsessive. Add good weather, a pinch of hedonism, a dose of culture, and it all adds up to that elusive prize: quality of life. In this collection of vignettes, take a ride in the slow lane with Taking Root in Provence, through la France profonde, ancient Roman cities, and that wonderful blend of the old and new worlds that is today's Provence.