Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Ring, Laurits Andersen --- Turner, Joseph Mallord William --- Constable, John --- romantiek --- landschappen --- 19de eeuw --- romantiek. --- landschappen. --- Turner, Joseph Mallord William. --- Constable, John. --- 19de eeuw.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. In particular, during the past dozen or so years many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular by tilting and cotilting theories. By here collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors' aim is to provide an aid to further research in this central topic in abstract algebra, and a reference for all whose research lies in this field.

Rings (Algebra) --- Modules (Algebra) --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Finite number systems --- Modular systems (Algebra) --- Finite groups --- Algebraic rings --- Ring theory --- Algebraic fields

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In a nutshell, the book deals with direct decompositions of modules and associated concepts. The central notion of "partially invertible homomorphisms”, namely those that are factors of a non-zero idempotent, is introduced in a very accessible fashion. Units and regular elements are partially invertible. The "total” consists of all elements that are not partially invertible. The total contains the radical and the singular and cosingular submodules, but while the total is closed under right and left multiplication, it may not be closed under addition. Cases are discussed where the total is additively closed. The total is particularly suited to deal with the endomorphism ring of the direct sum of modules that all have local endomorphism rings and is applied in this case. Further applications are given for torsion-free Abelian groups.

Modules (Algebra) --- RINGS (Algebra) --- Algebra. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Associative Rings and Algebras. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Mathematics --- Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. This book contains some important new contributions to the theory of structured ring spectra as well as survey papers describing these and relationships between them. One important aspect is the study of strict multiplicative structures on spectra and the development of obstruction theories to imposing strictly associative and commutative ring structures on spectra. A different topic is the transfer of classical algebraic methods and ideas, such as Morita theory, to the world of stable homotopy.

RINGS (Algebra) --- Spectral theory (Mathematics) --- Categories (Mathematics) --- Homotopy theory --- Rings (Algebra) --- Homotopy theory. --- Deformations, Continuous --- Topology --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Functor theory --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Algebraic rings --- Ring theory --- Algebraic fields

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.

Ordered algebraic structures --- Graded rings --- Associative rings --- Mathematical Theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Graded rings. --- Associative rings. --- Anneaux gradués --- Anneaux associatifs --- Algebra. --- Rings (Algebra). --- Category theory (Mathematics). --- Homological algebra. --- Group theory. --- Physics. --- Associative Rings and Algebras. --- Category Theory, Homological Algebra. --- Group Theory and Generalizations. --- Mathematical Methods in Physics. --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Groups, Theory of --- Substitutions (Mathematics) --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)