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This book collects and coherently presents the research that has been undertaken since the author’s previous book Module Theory (1998). In addition to some of the key results since 1995, it also discusses the development of much of the supporting material. In the twenty years following the publication of the Camps-Dicks theorem, the work of Facchini, Herbera, Shamsuddin, Puninski, Prihoda and others has established the study of serial modules and modules with semilocal endomorphism rings as one of the promising directions for module-theoretic research. Providing readers with insights into the directions in which the research in this field is moving, as well as a better understanding of how it interacts with other research areas, the book appeals to undergraduates and graduate students as well as researchers interested in algebra.
Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Associative rings. --- Rings (Algebra). --- Category theory (Mathematics). --- Homological algebra. --- Group theory. --- Associative Rings and Algebras. --- Category Theory, Homological Algebra. --- Group Theory and Generalizations. --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic rings --- Ring theory --- Algebraic fields --- Groups, Theory of --- Substitutions (Mathematics) --- Homological algebra --- Algebra, Abstract --- Homology theory
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Modules (Algebra) --- Endomorphism rings --- Direct sum decompositions
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Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, commutative rings, module and ring theory, and topological algebraic structures-providing more than 600 current references and 570 display equations for further exploration of the topic.
Abelian groups. --- Rings (Algebra) --- Modules (Algebra) --- Commutative groups --- Group theory --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Algebraic rings --- Ring theory --- Algebraic fields
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Àlgebra --- Topologia --- Poliedres --- Teoria de conjunts --- Aplicacions (Matemàtica) --- Categories (Matemàtica) --- Compactificacions --- Conjunts de Borel --- Dinàmica topològica --- Espais mètrics --- Espais vectorials topològics --- Grups de transformacions --- Grups topològics --- Jocs d'estratègia (Matemàtica) --- Politops --- Teoria de l'homotopia --- Teoria de la dimensió (Topologia) --- Teoria de la dualitat (Matemàtica) --- Teoria de grafs --- Teoria dels reticles --- Topologia algebraica --- Topologia combinatòria --- Topologia diferencial --- Varietats (Matemàtica) --- Varietats topològiques --- Xarxes (Matemàtica) --- Àlgebra lineal --- Matemàtica --- Àlgebra universal --- Algorismes --- Anàlisi combinatòria --- Àlgebra commutativa --- Anàlisi diofàntica --- Anàlisi espinorial --- Anàlisi p-àdica --- Àlgebra multilineal --- Àlgebres associatives --- Àlgebres no commutatives --- Combinatòria (Matemàtica) --- Congruències i residus --- Determinants (Matemàtica) --- Equacions --- Estructures algebraiques ordenades --- Factors (Àlgebra) --- Formes (Matemàtica) --- Interpolació (Matemàtica) --- Logaritmes --- Permutacions --- Representacions d'àlgebres --- Sèries (Matemàtica) --- Successions (Matemàtica) --- Teorema del binomi --- Teoria de grups --- Teoria de nombres --- Anàlisi matemàtica --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear
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This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of « roadmap » and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as « self-contained » chapters, the authors have tried to coordinate the texts in order to make them complementary. The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds d'Appui à l'Internationalisation of the Université catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.
Category theory. Homological algebra --- Ordered algebraic structures --- Algebra --- Topological groups. Lie groups --- Topology --- algebra --- wiskunde --- topologie
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Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches. .
Commutative rings --- Rings (Algebra) --- Commutative algebra. --- Commutative rings. --- Group theory. --- Associative rings. --- Rings (Algebra). --- Commutative Rings and Algebras. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Algebraic rings --- Ring theory --- Algebraic fields --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra
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Rings (Algebra) --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups
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Category theory. Homological algebra --- Ordered algebraic structures --- Algebra --- Topological groups. Lie groups --- Topology --- algebra --- wiskunde --- topologie
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