Modules over Noncommutative Rings, Homological Algebra and Noncommutative Geometry

Dear Colleagues,

This issue is devoted to the structure of noncommutative rings and modules over noncommutative rings and structure of noncommutative rings, homological algebra, their interactions with noncommutative geometry and sheaf theory, and applications in other areas, including mathematical physics. In particular, there may be rings with polynomial identities, division rings, Noetherian rings, Artinian rings, power associative rings, quadratic algebras, normed rings, topological rings, Jordan algebras, alternative rings, alternative algebras, non-associative rings, non-associative algebras, Cayley–Dickson algebras, filtered rings, Hochschild extension algebras, group algebras, quasigroup algebras, Noetherian modules, and Artinian modules. This may include studies of ring ideals, radicals, Jacobson radicals, prime ideals, idempotents, and involutive ideals. Other topics may be modules with regular singularities, holonomic modules, torsion modules, graded modules,  generators of modules, characterization of rings by properties of modules over them,  dual modules, normed modules, topological modules, modules with submodule lattice, hereditary modules, Rickartian modules, serial modules, (semi)distributive modules, sheaves of modules, graded sheaves, etc.

(Co)homologies may be of various types such as Hochschild (co)homology, Grothendieck (co)homology, Alexander cohomology, Steenrod homology, cyclic (co)homology, simplicial (co)homology, etc. This also may include derived functors, satellites, (co)homological dimension, complexes of modules, relations with operator theory and spectral theory of operators, relations with noncommutative geometry and mathematical physics, etc.

Manuscripts on vector spaces, topological vector spaces, modules, topological modules, their applications in PDEs, integral equations, mathematical analysis, functional analysis, mathematical physics also can be considered.

Prof. Dr. Sergey Ludkowski
Guest Editor

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