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1. |
Record Nr. |
UNISALENTO991003265999707536 |
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Autore |
Yengui, Ihsen |
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Titolo |
Constructive commutative algebra : projective modules over polynomial rings and dynamical Gröbner bases / Ihsen Yengui |
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Pubbl/distr/stampa |
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Cham [Switzerland] : Springer, c2014 |
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ISBN |
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Descrizione fisica |
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Collana |
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Lecture notes in mathematics, 0075-8434 ; 2138 |
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Classificazione |
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AMS 13-02 |
AMS 03F65 |
AMS 13C10 |
AMS 13D02 |
AMS 13P10 |
LC QA251.3.Y46 |
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Disciplina |
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Soggetti |
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Commutative algebra |
Gröbner bases |
Polynomial rings |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references (pages 259-268) and index |
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Nota di contenuto |
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Projective modules over polynomial rings ; Dynamical Gröbner bases ; Syzygies in polynomial rings over valuation domains ; Exercises ; Detailed solutions to the exercises |
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Sommario/riassunto |
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The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, |
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the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy |
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2. |
Record Nr. |
UNINA9910785707903321 |
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Autore |
López Ariel G. <1977-> |
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Titolo |
Shenoute of Atripe and the uses of poverty [[electronic resource] ] : rural patronage, religious conflict, and monasticism in late antique Egypt / / Ariel G. López |
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Pubbl/distr/stampa |
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Berkeley, Calif., : University of California Press, 2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (255 p.) |
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Collana |
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The Joan Palevsky imprint in classical literature |
Transformation of the classical heritage ; ; 50 |
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Disciplina |
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Soggetti |
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Coptic monasticism and religious orders - History |
Romans - Egypt |
Egypt History 30 B.C.-640 A.D |
Egypt Economic conditions 332 B.C.-640 A.D |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Revised dissertation--Princeton University, 2010. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction: "Rustic audacity" -- Loyal opposition -- A miraculous economy -- Rural patronage: holy and unholy -- The limits of intolerance -- Conclusion. |
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Sommario/riassunto |
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Shenoute of Atripe: stern abbot, loquacious preacher, patron of the poor and scourge of pagans in fifth-century Egypt. This book studies his numerous Coptic writings and finds them to be the most important literary source for the study of society, economy and religion in late antique Egypt. The issues and concerns Shenoute grappled with on a daily basis, Ariel Lopez argues, were not local problems, unique to one |
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small corner of the ancient world. Rather, they are crucial to interpreting late antiquity as a historical period-rural patronage, religious intolerance, the Christian care of the poor and the local impact of the late Roman state. His little known writings provide us not only with a rare opportunity to see the life of a holy man as he himself saw it, but also with a privileged window into his world. Lopez brings Shenoute to prominence as witness of and participant in the major transformations of his time. |
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