Extending the idea of compressed algebra to arbitrary socle-vectors
نویسنده
چکیده
In this paper we will study artinian quotients A = R/I of the polynomial ring R = k[x1, ..., xr], where k is a field of characteristic zero, the xi’s all have degree 1 and I is a homogeneous ideal of R. These rings are often referred to as standard graded artinian algebras. Before explaining the main results of this work, we establish some of the notation we will use: the h-vector of A is h(A) = h = (h0, ..., he),
منابع مشابه
Extending the idea of compressed algebra to arbitrary socle-vectors, II: cases of non-existence
متن کامل
When Are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?
Publications in Refereed Journals 1. I numeri di Fermat, Periodico di Matematiche, VII, 5 (1998), no. 2-3, 63–68 2. Some observations on the statistical independence and the distribution of zeros in the Selberg Class, Rend. Circ. Mat. Palermo (2), 52 (2003), no. 2, 211–223 3. Extending the idea of compressed algebra to arbitrary socle-vectors, J. Algebra 270 (2003), no. 1, 181–198 4. When are T...
متن کاملSocle Theory for Leavitt Path Algebras of Arbitrary Graphs
The main aim of the paper is to give a socle theory for Leavitt path algebras of arbitrary graphs. We use both the desingularization process and combinatorial methods to study Morita invariant properties concerning the socle and to characterize it, respectively. Leavitt path algebras with nonzero socle are described as those which have line points, and it is shown that the line points generate ...
متن کاملN ov 2 00 4 When is there a unique socle - vector associated to a given h - vector ? FABRIZIO
First we construct an interesting bijection between the set of h-vectors and the set of socle-vectors of artinian algebras. As a simple consequence, we find the minimum codimension that an artinian algebra with a given socle-vector can have. Then we address the main problem of this paper: determining when there is a unique socle-vector associated to a given h-vector. In Sections 3 and 5 we work...
متن کاملMinimal Resolution of Relatively Compressed Level Algebras
A relatively compressed algebra with given socle degrees is an Artinian quotient A of a given graded algebra R/c, whose Hilbert function is maximal among such quotients with the given socle degrees. For us c is usually a “general” complete intersection and we usually require that A be level. The precise value of the Hilbert function of a relatively compressed algebra is open, and we show that f...
متن کامل