Homological properties of some Weyl algebra extensions
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...
Le Nullstellensatz de Hilbert et les Polynomes à Valeurs Entières.
Les idéaux premiers de l'anneau des polynomes à valeurs entières.
Locally Polynomial Algebras are Symmetrie Algebras
Minimal degree solutions for the Bezout equation
Minimal degree solutions of polynomial equations
Note on strongly nil clean elements in rings
Let be an associative unital ring and let be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.
On a Retract of an Integral Domain.
On approximate roots of a polynomial.
On Armendariz rings.
On automorphisms of Weyl algebra
On Commutative Semigroups of Polynomials with Respect to Composition.