From the 1 of 10 linked papers with an AI index.
10 papers
Integral closure for (additively idempotent) semirings
Netanel Friedenberg, Kalina Mincheva
The paper studies various notions of integrality for (additively idempotent) semirings, compares them, and proves a Cayley‑Hamilton theorem in this setting, with applications to co…
Geometric classification of primes modulo a (bend) congruence
Netanel Friedenberg, Kalina Mincheva
In this paper we continue the program to develop the algebraic foundations of tropical (algebraic) geometry. We give strong characterizations of prime congruences containing a give…
Prime ideals in the Boolean polynomial semiring
Kalina Mincheva, Naufil Sakran
In this article, we disprove a conjecture of F. Alarcón and D. Anderson and give a complete classification of the prime ideals in the one variable polynomial semiring with coeffic…
Varieties of prime tropical ideals and the dimension of the coordinate semiring
Dániel Joó, Kalina Mincheva
In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime idea…
Geometric interpretation of valuated term (pre)orders
Netanel Friedenberg, Kalina Mincheva
Valuated term orders are studied for the purposes of Gröbner theory over fields with valuation. The points of a usual tropical variety correspond to certain valuated terms preorde…
Representation theory over semifields
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study and classify representations of a torsion group over an idempotent semifield with special attention on the case over the Boolean semifield . In subsequent…