Homological Algebra Of Semimodules And Semicont... May 2026

Unlike traditional modules over a ring, are defined over semirings (like the

Frequently used to study the global sections of semimodule sheaves on tropical varieties. 3. Semicontinuity and Stability Homological Algebra of Semimodules and Semicont...

The rank or homological dimension of a semimodule often drops at specific points of a parameter space, mirroring the behavior of coherent sheaves in algebraic geometry. Unlike traditional modules over a ring, are defined

algebra). Because semimodules lack additive inverses, they do not form an abelian category. This necessitates a shift from exact sequences to and kernel-like structures based on congruences. 2. Derived Functors in Non-Additive Settings Unlike traditional modules over a ring

Constructing resolutions using free semimodules or injective envelopes (like the "max-plus" analogues of vector spaces).