# Algebra

The members working in Algebra in this Department are Marco D'Anna, Carmelo Antonio Finocchiaro and Vincenzo Micale. They mainly work on commutative algebra and semigroups theory.

**Semigroups:** we investigate numerical semigroups and good semigroups, that are particular subsemigrups of NxNx...xN, which include value semigrups of curve singularities (D'Anna, Micale).

**One-dimensional Rings and curve singularities:** we investigate numerical semigroup rings, analytically irreducible domains and, more in general, analytically unramified reduced rings. The investigation is performed dealing with their associated semigroups. We also investigate the properties of their associated graded rings (D'Anna, Micale)

**Extensions of rings satisfying prescribed properties:** duplication of a ring along an ideal, amalgamation algebras, quadratic quotients of Rees algebras (D'Anna, Finocchiaro)

**Algorithms:** for the computation of the semigroups of orders of formal power series and the semigroups of degrees of polynomials (V. Micale)

**Topological methods in Commutative Algebra:** spectral spaces; relationships between topological properties of spaces of rings and their modules and algebraic properties. Multiplicative ideal theory (Finocchiaro).

##### Contacts

prof. Andrea Giacobbe