21 citations · 24 across the 17 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…
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…