Ideals in rings of integer valued polynomials.
Ideaux de polynomes et ideaux de valeurs.
Idéaux premiers de Goldman
Idempotent semigroups and tropical algebraic sets
The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup structure. We address the question of the geometry of idempotent semigroups, in particular, tropical algebraic sets carrying the structure of a commutative idempotent semigroup. We show that commutative idempotent semigroups are contractible, that systems of tropical...
Integer-valued polynomials on algebras: a survey
We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.
Integral closure of monomial ideals on regular sequences.
Inversion of Monic polynomials and Existence of Unimodular Elements (II).
Invertible ideals and Gaussian semirings
In the first section, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Prüfer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Prüfer semirings in terms of some identities over its ideals such as for all ideals , of . In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable family...