21 citations · 24 across the 17 of their papers we have counts for
18 papers
Integral closure for (additively idempotent) semirings
Netanel Friedenberg, Kalina Mincheva
In commutative ring theory there are multiple equivalent definitions of integrality. These notions diverge when working with idempotent semirings. In this paper we present these di…
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 coeffici…
Matroidal representations of low rank
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study tropical subrepresentations of the Boolean regular representation of a finite group . These are equivalent to the matroids on ground set for which l…
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…
Tropical representations and valuated matroids
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We explore several facets of tropical subrepresentations of a linear representation of a group over the tropical semifield . A key role in the study of tropical subrepr…
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…
Equivariant vector bundles on toric schemes over semirings
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric ve…
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 preorder…
Tropical adic spaces I: The continuous spectrum of a topological semiring
Netanel Friedenberg, Kalina Mincheva
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a t…
-semiring pairs
Jaiung Jun, Kalina Mincheva, Louis Rowen
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investi…
Vector bundles on tropical schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, whic…
Homology of systemic modules
Jaiung Jun, Kalina Mincheva, Louis Rowen
We develop the rudiments of a tropical homology theory, based on "triples" and "systems." Results include a version of Schanuel's lemma, projective dimension, the homology semi-mod…
Projective systemic modules
Jaiung Jun, Kalina Mincheva, Louis Rowen
We develop the basic theory of projective modules and splitting in the more general setting of systems. Systems provide a common language for most tropical algebraic approaches inc…
Picard groups for tropical toric schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
From any monoid scheme (also known as an -scheme) one can pass to a semiring scheme (a generalization of a tropical scheme) by scalar extension to an idempo…
Computing toric degenerations of flag varieties
Lara Bossinger, Sara Lamboglia, Kalina Mincheva +1
We compute toric degenerations arising from the tropicalization of the full flag varieties and embedded in a product of Grassmannians. For $…
On the dimension of polynomial semirings
Dániel Joó, Kalina Mincheva
In our previous work, motivated by the study of tropical polynomials, a definition for prime congruences was given for an arbitrary commutative semiring. It was shown that for addi…
Prime congruences of idempotent semirings and a Nullstellensatz for tropical polynomials
Dániel Joó, Kalina Mincheva
A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ide…