Research (versione italiana)

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

• The polynomial closure is not topological
  (with Giulio Peruginelli)
  Journal of Pure and Applied Algebra 226(12) (2022), 107133.
  doi:10.1016/j.jpaa.2022.107133


• Isolated points of the Zariski space
  New York Journal of Mathematics 28 (2022), 800-823.


• The derived sequence of a pre-Jaffard family
  Mediterranean Journal of Mathematics 19(4) (2022), 146.
  doi:10.1007/s00009-022-02028-z


• Metrizability of spaces of valuation domains associated to pseudo-convergent sequences
  (with Giulio Peruginelli)
  Journal of Algebra and Its Applications (to appear).
  doi:10.1142/S0219498823500469


• Radicals of principal ideals and the class group of a Dedekind domain
  Pacific Journal of Mathematics 314(1) (2021), 219-231.
  doi:10.2140/pjm.2021.314.219


• Extending valuations to the field of rational functions using pseudo-monotone sequences
  (with Giulio Peruginelli)
  Journal of Algebra 586 (2021), 756-786.
  doi:10.1016/j.jalgebra.2021.07.004


• Asymptotic for the number of star operations on one-dimensional Noetherian domains
  Journal of the Korean Mathematical Society 58(5) (2021), 1239-1260.
  doi:10.4134/JKMS.j200543


• The Golomb space is topologically rigid
  (with Taras Banakh e Sławomir Turek)
  Commentationes Mathematicae Universitatis Carolinae 62(3) (2021), 347-360.
  doi:10.14712/1213-7243.2021.023


• Multiplicative properties of Integer valued Polynomials over split-quaternions
  (with Antonio Cigliola e Francesca Tartarone) Communications in Algebra 49(3) (2021), 1338-1351.
  doi:10.1080/00927872.2020.1834572


• Multiplicative closure operations on ring extensions
  Journal of Pure and Applied Algebra 225(4) (2021), 106555.
  doi:10.1016/j.jpaa.2020.106555


• Suprema in spectral spaces and the constructible closure
  (with Carmelo Finocchiaro)
  New York Journal of Mathematics 26 (2020), 1064-1092.
  


• Wilf's conjecture for numerical semigroups with large second generator
  Journal of Algebra and Its Applications (2021), no. 11, 2150197.
  doi:10.1142/S0219498821501978


• Decomposition and classification of length functions
  Forum Mathematicum 32(5) (2020), 1109-1129.
  doi:10.1515/forum-2018-0168


• The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences
  (with Giulio Peruginelli)
  Transactions of the American Mathematical Society 373(11) (2020), 7959-7990.
  doi:10.1090/tran/8185


• An ultrapower analogue of the Kronecker function ring
  (with Alan Loper)
  Fundamenta Mathematicae 252 (2021), no. 1, 103–119.
  doi:10.4064/fm833-4-2020


• The Golomb topology of polynomial rings
  Quaestiones Mathematicae 44 (2021), no. 4, 447-468.
  doi:10.2989/16073606.2019.1704904


• The Golomb topology on a Dedekind domain and the group of units of its quotients
  Topology and Its Applications 293 (2020), 107101.
  doi:10.1016/j.topol.2020.107101


• Topological properties of subsets of the Zariski space
  Gładki P., Koenigsmann J., Koprowski P., Kubiś W., Kučera R., Kuhlmann F.-V., Mišík L. (editors), Proceedings of the 5th Joint Conferences on Algebra, Logic and Number Theory, Banach Center Publications 121, Polish Academy of Sciences (2020)
  doi:10.4064/bc121-15


• When two principal star operations are the same
  Facchini A., Fontana M., Geroldinger A., Olberding B. (editors), Advances in Rings, Modules and Factorizations. Rings and Factorizations 2018, Springer Proc. Math. Stat. 321, Springer (2020).
  doi:10.1007/978-3-030-43416-8_17


• The number of star operations on numerical semigroups and on related integral domains
  Barucci V., Chapman S., D'Anna M., Fröberg R. (editors) Numerical Semigroups. Springer INdAM Series, vol 40 (2020).
  doi:10.1007/978-3-030-40822-0_17


• When the Zariski space is a Noetherian space
  Illinois Journal of Mathematics 63(2) (2019), 299-316
  doi:10.1215/00192082-7773701


• 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
  Corrigendum


• 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 12 (2020), no. 4, 581–602.


• 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
  (with 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 $N^n$
  Journal of Algebra and Its Applications 17 (2018), no. 11, 1850205
  doi:10.1142/S0219498818502055


• Towards a classification 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 11 (2019), no. 3, 401–431.


• 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


• Distinguished classes of ideal spacs and their topological properties
  (with Amartya Goswami e Carmelo Finocchiaro)
  Communications in Algebra (to appear)


• Almost Dedekind domains without radical factorization
  Forum Mathematicum (to appear)


• Radical semistar operations
  Communications in Algebra (to appear)

Preprint

• Polynomially Independent Subsets and Generalized Nagata Rings (with Alan Loper)


• Localizations of integer-valued polynomials and of their Picard group


• The Golomb topology of polynomial rings, II

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