Pith. sign in

Title resolution pending

· 2026 · math.RA · arXiv 2602.19209

1 Pith paper cite this work. Polarity classification is still indexing.

1 Pith paper citing it
open full Pith review browse 1 citing papers arXiv PDF

Title metadata for this work has not finished resolving. The hub is built from the citation graph; the title resolver retries DOI and OpenAlex on its next pass.

abstract

We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main features are a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, and a ``surpassing relation,'' taking the place of equality, which permit generalizations of the classical algebraic theory to polynomials and their roots, algebraic geometry, matrices, linear algebra, varieties, categories, and module theory. The ``pair'' $(\mcA,\mcA_0)$ is studied along the lines of universal algebra.

fields

math.RA 1

years

2026 1

verdicts

CONDITIONAL 1

representative citing papers

Roots of polynomials over semirings and hyperfields

math.RA · 2026-06-11 · conditional · novelty 5.0 · 3 refs

Over semiring/hyperfield pairs with a surpassing relation, tangible polynomials can be split into linear factors, and zero-sum-free pairs extend to integrally closed pairs.

citing papers explorer

Showing 1 of 1 citing paper.

  • Roots of polynomials over semirings and hyperfields math.RA · 2026-06-11 · conditional · none · ref 14 · 3 links · internal anchor

    Over semiring/hyperfield pairs with a surpassing relation, tangible polynomials can be split into linear factors, and zero-sum-free pairs extend to integrally closed pairs.