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Facets of module theory over semirings

· 2024 · math.AG · arXiv 2405.18645

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abstract

We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual definitions of line bundle do agree. We also show that the narrow class group of a number field can be recovered as a reflexive Picard group of its subsemiring of totally nonnegative algebraic integers.

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Representation theory over semifields

math.RT · 2024-11-29 · conditional · novelty 8.0

For a finite or torsion group G over an idempotent semifield, representations are in one-to-one correspondence with G-sets.

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  • Representation theory over semifields math.RT · 2024-11-29 · conditional · none · ref 1 · internal anchor

    For a finite or torsion group G over an idempotent semifield, representations are in one-to-one correspondence with G-sets.