And Semicont...: Homological Algebra Of Semimodules

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

The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations. Homological Algebra of Semimodules and Semicont...

It connects to the Lusternik-Schnirelmann category in idempotent analysis, where semicontinuity helps track the stability of eigenvalues in max-plus linear systems. 4. Applications: Tropical Geometry Unlike traditional modules over a ring, are defined

This framework provides the "linear algebra" for tropical varieties. Just as homological algebra helps classify manifolds, semimodule homology helps classify and understand the intersections of tropical hypersurfaces. Unlike traditional modules over a ring

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

The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations.

It connects to the Lusternik-Schnirelmann category in idempotent analysis, where semicontinuity helps track the stability of eigenvalues in max-plus linear systems. 4. Applications: Tropical Geometry

This framework provides the "linear algebra" for tropical varieties. Just as homological algebra helps classify manifolds, semimodule homology helps classify and understand the intersections of tropical hypersurfaces.

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