Publications

Published/accepted papers

• 1. Parametrizing over $\Z$ integral values of polynomials over $\Q$, with U. Zannier. Comm. Algebra, 38 (2010), no. 1, 119-130. [pdf] [doi]

• 2. On some notions of good reduction for endomorphisms of the projective line, with J.-K. Canci and D. Tossici, Manuscripta Math. 141 (2013), no. 1-2, 315-331. [pdf] [doi] [Arxiv]

• 3. Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power, J. Algebra 398 (2014), 227-242. [pdf] [doi] [Arxiv] (Open Access)

• 4. Integer-valued polynomials over matrices and divided differences, Monatsh. Math. 173 (2014), no. 4, 559-571.  [pdf] [doi] [Arxiv] 

• 5. Integral-valued polynomials over sets of algebraic integers of bounded degree, J. Number Theory 137 (2014) 241-255. [pdf]  [doi] [Arxiv] (Open Access)

• 6. Factorization of integer-valued polynomials with square-free denominator, Comm. Algebra, 43 (2015), no. 1, 197-211.   [pdf] [doi] [Arxiv]

• 7. The ring of polynomials integral-valued over a finite set of integral elements, J. Commut. Algebra 8 (2016), no. 1, 113-141. [pdf] [doi] [Arxiv]

• 8. Polynomial overrings of  $\Int(\Z)$, with J.-L. Chabert, J. Commut. Algebra 8 (2016), no. 1, 1-28. [pdf] [doi] [Arxiv] 

• 9. Properly Integral Polynomials over the Ring of Integer-Valued Polynomials on a Matrix Ring, with N. J. Werner, J. Algebra 460 (2016) 320-339. [doi] [Arxiv] (Open Access)

• 10. The lattice of primary ideals in orders in quadratic number fields, with. P. Zanardo, Int. J. Number Theory 12 (2016), no. 7, 2025-2040. [doi] [Arxiv](Open Access)

• 11. Non-triviality Conditions for Integer-valued Polynomial Rings on Algebras, with N. J. Werner, Monatsh. Math. 183 (2017), no. 1, 177-189. [pdf (published)] [doi] [Arxiv]

• 12. Galois structure on integral valued polynomials, with B. Heidaryan and M. Longo, J. Number Theory 171 (2017), 198-212. [doi] [Arxiv] (Open Access)

• 13. Transcendental extensions of a valuation domain of rank one, Proc. Amer. Math. Soc. 145 (2017), no. 10, 4211-4226. [doi] [Arxiv]

• 14. Adelic versions of the Weierstrass approximation Theorem, with J.-L. Chabert, J. Pure Appl. Algebra 222 (2018), no. 3, 568-584. [doi] [Arxiv]

• 15. Decomposition of Integer-valued Polynomial Algebras, with N. J. Werner, J. Pure Appl. Algebra 222 (2018), no. 9, 2562-2579. [doi] [Arxiv]

• 16. Maximal subrings and Covering Numbers of Finite Semisimple Rings, with N. J. Werner, Comm. Algebra 46 (2018), no. 11, 4724-4738 . [doi]

• 17. Prufer intersection of valuation domains of a field of rational functions, J. Algebra 509 (2018), 240-262. [doi] [Arxiv]

• 18. The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences, with D. Spirito, Trans. Amer. Math. Soc. 373 (2020), no. 11, 7959–7990. [doi] [arXiv] 

• 19. Extending valuations to the field of rational functions using pseudo-monotone sequences, with D. Spirito, J. Algebra 586 (2021), 756-786. [doi] [arXiv]

• 20. The polynomial closure is not topological, with D. Spirito, J. Pure Appl. Algebra 226 (2022), no. 12, 107133.  [doi] [arXiv]

• 21. Metrizability of spaces of valuation domains associated to pseudo-convergent sequences,  with D. Spirito, J. Algebra Appl. 22 (2023), no. 2, 2350046. [doi] [arXiv]

• 22. Polynomial Dedekind domains with finite residue fields of prime characteristic, Pacific J. Math. 324 (2023), no. 2, 333-351. [doi] [arXiv] (Open Access)

Conference Proceedings (with referee)

• i). Parametrization of integral values of polynomials, Actes des rencontres du CIRM, 2 no. 2: Third International Meeting on Integer-Valued Polynomials (2010), p. 41-49. [doi]

• ii). Integral closure of rings of integer-valued polynomials on algebras, with Nicholas J. Werner, in "Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 2016, pp. 293-305, ISBN 978-1-4939-0924-7 [Link], [pdf] [doi] [Arxiv]

• iii). Idempotent pairs and PRINC domains, with L. Salce and P. Zanardo, in ``Multiplicative Ideal Theory and Factorization Theory - Commutative and Non-Commutative Perspectives'', S. Chapman, M. Fontana, A. Geroldinger, and B. Olberding, Editors, Springer Verlag Publisher (2016), pp. 309-322. ISBN 978-3-319-38855-7 [Link] [pdf] [doi] [Arxiv]

Submitted

• Stacked Pseudo-Convergent Sequences and Polynomial Dedekind Domains. [arXiv]

• Key polynomials in terms of ultrametric balls, with J. Novacoski and E. Nart. [arXiv]

Preprint/in preparation

• Nontriviality of rings of integral-valued polynomials, with N. J. Werner.

• Skolem properties of generalized rings of integer-valued polynomials.

• Fixed divisor of polynomials over matrices.

• Formal parametrizations of algebraic curves, preprint Department of Mathematics of the University of Pisa, March 2008.

• Evaluation of integer-valued polynomials on algebraic integers, preprint.