The spectrum of prime congruences of a pair

Fuente: arXiv
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Main Author: Rowen, Louis H.
Format: Preprint
Published: 2024
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author Rowen, Louis H.
author_facet Rowen, Louis H.
contents Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,'' which include supertropical semirings and various classes of hyperrings. Our main result is that the Joo-Mincheva spectrum can be embedded into the prime spectrum of a semiring pair, and the mapping is onto when the pair satisfies a mild restriction which we call ``positive $e$-type.''
format Preprint
id arxiv_https___arxiv_org_abs_2412_18559
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The spectrum of prime congruences of a pair
Rowen, Louis H.
Rings and Algebras
Primary 08A30, 16Y60, Secondary 08A05, 15A80, 14T10
Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,'' which include supertropical semirings and various classes of hyperrings. Our main result is that the Joo-Mincheva spectrum can be embedded into the prime spectrum of a semiring pair, and the mapping is onto when the pair satisfies a mild restriction which we call ``positive $e$-type.''
title The spectrum of prime congruences of a pair
topic Rings and Algebras
Primary 08A30, 16Y60, Secondary 08A05, 15A80, 14T10
url https://arxiv.org/abs/2412.18559