Note on convergence and orders of vanishing along curves.
Note on modules over Prüfer domains.
Note on projective modules.
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.
Note on the transitivity of pure essential extensions
Note sur la méthode d'élimination de Bezout
Note sur un article de Sharif et Woodcock
H. Sharif et C. Woodcock donnent dans [26] une caractérisation des séries formelles à coefficients dans un corps de caractéristique non nulle et algébriques sur ; ils en déduisent simplement l’algébricité du produit de Hadamard ou des diagonales de séries algébriques. (Ces résultats ont aussi été obtenus par T. Harase [14]). Nous donnons ici une démonstration légèrement différente de leur théorème et montrons comment on peut en déduire une généralisation intéressante de la notion de -substitution...
Notes on an extension of Krull's principal ideal theorem
Notes on annihilator conditions in modules over commutative rings.
Notes on compact rings with open radical
Notes on generalizations of Bézout rings
In this paper, we give new characterizations of the --Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non--Bézout --Bézout rings and examples of non--Bézout --Bézout rings.
Notes on radical filters of ideals
Notes on structure of complete discrete valuation rings.
Notes on the multiplicity conjecture.
New cases of the multiplicity conjecture are considered.
Numerical characters of graded algebras
This is the summary of the plenary talk I gave in Milan at the XVII Meeting of the Unione Matematica Italiana. We focus on some relevant numerical characters of the standard graded algebras and, in some case, we explain their geometric meaning.
Numerical invariants of liasion classes.
Numerical semigroups of maximal and almost maximal length.
Numerical semigroups with a monotonic Apéry set
We study numerical semigroups with the property that if is the multiplicity of and is the least element of congruent with modulo , then . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.