Carmelo Antonio FINOCCHIARO

Ricercatore di ALGEBRA [MAT/02]


Carmelo Antonio Finocchiaro è in servizio presso l'Università di Catania dal mese di Dicembre del 2018, quale ricercatore a tempo determinato (tipo b) in Geometria e Algebra (S.S.D. MAT/02). 

Nel 2017-2018 è stato ricercatore a tempo determinato (tipo a) in Geometria e Algebra (S.S.D. MAT/02) presso il Dipartimento di Matematica dell'Università degli Studi di Padova. 

Insegna nel corso di Laurea Magistrale in Matematica.

Svolge attività di ricerca principalmente in Algebra Commutativa e Topologia Generale. 

• Properties of chains of prime ideals in an almalgamated algebra along
an ideal [with M. D’Anna and M. Fontana], J. Pure Appl. Algebra
214 (2010), no. 9, 1633– 1641.


• Star-invertibility and t-finite character in integral domains [with G.
Picozza and F. Tartarone] J. Algebra Appl. 10 (2011) n. 4, 755 –
769.


• Prüfer-like conditions on an amalgamated algebra along an ideal.
Houston J. Math, 40, volume 1 (2014), 63-79.


• The constructible topology on spaces of valuation domains [with M.
Fontana e K.A. Loper], Trans. Amer. Math. Soc. 365, n. 12 (2013)
6199–6216.


• Ultrafilter and constructible topology on spaces of valuation domains
[with M. Fontana and K. A. Loper], Comm. Algebra, 41, Issue 05,7
pages 1825- 1835 (2013).


• Spectral spaces and ultrafilters, Comm. Algebra, Volume 42, Issue
4, 1496-1508 (2014).


• Some topological considerations on semistar operations [with D.
Spirito] J. Algebra 409 (2014), 199–218.


• On a topological characterization of Prüfer v-multiplication domains
among essential domains [with F. Tartarone], J. Commutative Alge-
bra, 8 (2016), no. 4, 513–536.


• New algebraic properties of an amalgamated algebra along an ideal
[with M. D’Anna and M. Fontana] Comm. Algebra, 44 (2016), no.
5, 1836–1851.


• Amalgamated algebras along an ideal, [with M. D’Anna and M. Fon-
tana], Commutative algebra and its applications, 155–172, Walter de
Gruyter, Berlin, (2009).


• Some closure operations in Zariski-Riemann spaces of valuation do-
mains: a survey [with M. Fontana and K.A. Loper], in ”Commutati-
ve Algebra: Recent Advancesin Commutative Rings, Integer-Valued
Polynomials and Polynomial Functions” (Proceedings of the Graz
Conference) Springer Verlag 2014.


• New distinguished classes of spectral spaces:a survey [with M. Fon-
tana and D. Spirito] in ”Multiplicative Ideal Theory and Factoriza-
tion Theory - Commutative and Non-Commutative Perspectives”,
Springer Verlag Publisher, 2016.


• The strong ultrafilter topology on spaces of ideals [with K.A. Loper]
J. Algebra, 461 (2016), 226–243.


• Topology, intersection of modules and flat modules [with D. Spirito],
Proc. Amer. Math. Soc., 144 (2016), no. 10, 4125-4133.


• Spectral spaces of semistar operations [with M. Fontana and D.
Spirito] J. Pure Appl. Algebra, 220 (2016), no. 8, 2897–2913.


• A topological version of Hilbert’s Nullstellensatz [with M. Fontana
and D. Spirito], J. Algebra, 461 (2016), 25–41.


• Invertibility of ideals in Prüfer extensions [with F. Tartarone] Comm.
Algebra 45 (2017), no. 10, 4521–4527.


• Topological properties of semigroup primes of a commutative ring
[with M. Fontana and D. Spirito] Beiträge zur Algebra und Geome-
trie, 58 (2017), no. 3, 453–476.


• A construction of Prüfer rings involving quotients of Rees algebras,
J. Algebra Appl., 17 (2018), no. 6, 1850098, 16 pp.


• The upper Vietoris topology on the space of inverse closed subsets of8
a spectral space and applications [with M. Fontana and D. Spirito]
Rocky Mountain J. Math., 48 5 (2018), 1551-1583.


• Bi-amalgamated constructions [with F. Campanini], J. Algebra Ap-
pl., to appear (https://doi.org/10.1142/S0219498819501482).

L'attività di ricerca di Carmelo Antonio Finocchiaro si svolge principalmente nell'ambito delle applicazioni della Topologia Generale all'Algebra Commutativa, più specificamente alla Teoria Moltiplicativa degli Ideali. In particolare, si occupa di spazi spettrali, spazi topologici di anelli e moduli, teoria delle valutazioni. Inoltre si occupa di costruzioni di algebre con date proprietà, e.g., prodotti fibrati, amalgamazioni di anelli e opportuni quozienti di algebre di Rees.