6 citations · 36 across the 42 of their papers we have counts for
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Extending the idea of compressed algebra to arbitrary socle-vectors, II: cases of non-existence
Fabrizio Zanello
This paper is the continuation of the previous work on generalized compressed algebras (GCA's). First we exhibit a new class of socle-vectors which admit a GCA (whose -vecto…
Extending the idea of compressed algebra to arbitrary socle-vectors
Fabrizio Zanello
Fix a codimension and a socle-vector . Is there an (entry by entry) maximal -vector among the -vectors of all the (standard graded artinian) algebras having data $…
When are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?
Fabrizio Zanello
It has been a well-known fact since Euclid's time that there exist infinitely many rational primes. Two natural questions arise: In which other rings, sufficiently similar to the i…
Stanley's theorem on codimension 3 Gorenstein -vectors
Fabrizio Zanello
In this note we supply an elementary proof of the following well-known theorem of R. Stanley: the -vectors of Gorenstein algebras of codimension 3 are SI-sequences, i.e. are sym…
When is there a unique socle-vector associated to a given -vector?
Fabrizio Zanello
First, we construct a bijection between the set of -vectors and the set of socle-vectors of artinian algebras. As a corollary, we find the minimum codimension that an artinian a…
Level algebras of type 2
Fabrizio Zanello
In this paper we study standard graded artinian level algebras, in particular those whose socle-vector has type 2. Our main results are: the characterization of the level -vecto…