88 research outputs found
Properties of chains of prime ideals in an amalgamated algebra along an ideal
Let be a ring homomorphism and let be an ideal of . In
this paper, we study the amalgamation of with along with respect to
(denoted by ), a construction that provides a general frame
for studying the amalgamated duplication of a ring along an ideal, introduced
and studied by D'Anna and Fontana in 2007, and other classical constructions
(such as the , the and the constructions). In
particular, we completely describe the prime spectrum of the amalgamated
duplication and we give bounds for its Krull dimension.Comment: J. Pure Appl. Algebra (to appear
The numerical duplication of a numerical semigroup
In this paper we present and study the numerical duplication of a numerical
semigroup, a construction that, starting with a numerical semigroup and a
semigroup ideal , produces a new numerical semigroup, denoted by
S\Join^b\E (where is any odd integer belonging to ), such that
S=(S\Join^b\E)/2. In particular, we characterize the ideals such that
is almost symmetric and we determine its type.Comment: 17 pages. Accepted for publication on: Semigroup Foru
A family of quotients of the Rees algebra
A family of quotient rings of the Rees algebra associated to a commutative
ring is studied. This family generalizes both the classical concept of
idealization by Nagata and a more recent concept, the amalgamated duplication
of a ring. It is shown that several properties of the rings of this family do
not depend on the particular member.Comment: 17 pages. To appear on "Communications in Algebra
Arf characters of an algebroid curve
Two algebroid branches are said to be equivalent if they have the same
multiplicity sequence. It is known that two algebroid branches and are
equivalent if and only if their Arf closures, and have the same value
semigroup, which is an Arf numerical semigroup and can be expressed in terms of
a finite set of information, a set of characters of the branch.
We extend the above equivalence to algebroid curves with branches. An
equivalence class is described, in this more general context, by an Arf
semigroup, that is not a numerical semigroup, but is a subsemigroup of . We express this semigroup in terms of a finite set of information, a set
of characters of the curve, and apply this result to determine other curves
equivalent to a given one.Comment: 17 page
- …