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My research deals with problems in commutative algebra, in
particular on the study of algebraic structures from a topological
point of view. I am also interested in the study of sets of closure
operations (star and semistar operations) on integral domains and
numerical semigroups.
Papers
- When the Zariski space is a
Noetherian space
Illinois Journal of Mathematics (to appear)
- Vector subspaces of finite
fields and star operations on pseudo-valuation domains
Finite Fields and Their Applications 56
(2019), 17-30
doi:
10.1016/j.ffa.2018.11.001
- Star operations on Kunz
domains
International Electronic Journal of Algebra 25 (2019), 171-185
doi:
10.24330/ieja.504142
- The Zariski topology on
sets of semistar operations without finite-type assumptions
Journal of Algebra 513 (2018), 27-49
doi:
10.1016/j.jalgebra.2018.07.021
- Topological
properties of localizations, flat overrings and sublocalizations
Journal of Pure and Applied Algebra 223(3)
(2019), 1322-1336
doi:
10.1016/j.jpaa.2018.06.008
- The sets of star and
semistar operations on semilocal Prüfer domains
Journal of Commutative Algebra (to appear)
- Calculating the
density of solutions of equations related to the Pólya-Ostrowski group
through Markov chains
Acta Arithmetica 186(4) (2018), 319-335
doi:
10.4064/aa170605-6-3
- The upper Vietoris topology on the space
of inverse-closed
subsets of a spectral space and applications
(con Carmelo Finocchiaro e Marco Fontana)
Rocky Mountain Journal of Mathematics 48(5), 1551-1583
doi:10.1216/RMJ-2018-48-5-1551
- Embedding
the set of non-divisorial ideals of a numerical semigroup into
Journal of Algebra and Its Applications (to appear)
doi:10.1142/S0219498818502055
- Towards
a classication of stable semistar operations on a Prüfer domain
Communications in Algebra 46(4) (2018), 1831-1842
doi:10.1080/00927872.2017.1360329
- Jaffard
families and localizations of star operations
Journal of Commutative Algebra 11(2)
(2019), 265-300
doi:10.1216/JCA-2019-11-2-265
- Star
operations on numerical semigroups: antichains and explicit results
Journal of Commutative Algebra (to appear)
- Non-compact
subsets of the Zariski space of an integral domain
Illinois Journal of Mathematics 60(3-4) (2017), 791-809
- Topological properties
of semigroup primes of a commutative ring
(with Carmelo Finocchiaro e Marco Fontana)
Beiträge zur Algebra und Geometrie 58(3) (2017), 453-476
doi:10.1007/s13366-017-0340-z,
MR3683022
- Topology,
intersections and flat modules
(with Carmelo Finocchiaro)
Proceedings of the Americal Mathematical Society 144(10)
(2016), 4125-4133
doi:10.1090/proc/13131,
MR3531166
- A
topological version of Hilbert's Nullstellensatz
(with Carmelo Finocchiaro e Marco Fontana)
Journal of Algebra 461 (2016), 25-41
doi:10.1016/j.jalgebra.2016.04.020,
MR3513063
- Spectral
spaces of semistar operations
(with Carmelo Finocchiaro e Marco Fontana)
Journal of Pure and Applied Algebra 220(8) (2016), 2897-2913
doi:10.1016/j.jpaa.2016.01.008,
MR3471195
- New
distinguished classes of spectral spaces: a survey
(with Carmelo Finocchiaro e Marco Fontana)
S. Chapman, M. Fontana, A. Geroldinger, B. Olberding (editor), Multiplicative
Ideal Theory and Factorization Theory: Commutative and Non-Commutative
Perspectives, Capitolo 5 (2016)
doi:10.1007/978-3-319-38855-7_5,
MR3565806
- Star
operations on numerical semigroups: The multiplicity 3 case
Semigroup Forum 91(2) (2015), 476-494
doi:10.1007/s00233-014-9643-7,
MR3401798
- Star
operations on numerical semigroups
Communications in Algebra 43(7) (2015), 2943-2963
doi:10.1080/00927872.2014.908201,
MR3354072
- Some
topological considerations on semistar operations
(with Carmelo Finocchiaro)
Journal of Algebra 409 (2014), 199-218
doi:10.1016/j.jalgebra.2014.04.002,
MR3198840
Preprint
PhD thesis
My PhD thesis deals with three different subjects, different but
related, all linked to the study of closure operations from a
structural point of view. The first chapter is centered on the study of
star operations on numerical semigroups (in particular, the study of
the cardinality of this set); the second studies semistar operations
(and related spaces, e.g. spaces of overrings) from a topological point
of view; the third deals with the possibility of writing the set of
star oeprations on an integral domain D through the sets of star
operations on overrings of D.
Thesis, abstract