Let K be a field with char(K)=0. For partition λ of n∈N, let IλSp the ideal R=K[x1,…,xn] generated by all Specht polynomials shape λ. These ideals have been studied from several points view (and under names). Using advanced tools representation theory, Berkesch Zamaere et al. [1] constructed minimal free resolution I(n−d,d)Sp except differential maps. The present paper constructs maps, and also...

Introduction. In this paper we give a sufficient condition that an algebra have a minimal left (or right) ideal. Specifically, we prove that if A is a complex semisimple Banach algebra with the property that the spectrum of every element in A is at most countable, then A has a minimal left ideal. If A is an ^4*-algebra, we prove that A has a minimal left ideal if the spectrum of every self-adjo...

In [1] it is shown that every monomial ideal admits a simplicial resolution (Taylor’s resolution) and that some minimal free resolutions are supported in simplicial complexes (Scarf ideals, monomial regular sequences). This idea is generalized in [2] where cellular resolutions are introduced. The authors show that every monomial ideal admits a resolution supported in a regular cell complex (the...

In the theory of monomial ideals of a polynomial ring S over a field k, it is convenient that for each such ideal I there is a standard free resolution, so called Taylor resolution, that can be canonically constructed from the minimal system of monomial generators of I (see [7], p.439 and section 2). On the other hand no construction of a minimal resolution for an arbitrary monomial ideal has b...

Abstract Let Δ be a one‐dimensional simplicial complex. the Stanley–Reisner ideal of Δ. We prove that for all and intermediate ideals J generated by some minimal generators , we have

Let SI be a finite dimensional algebra with unit element over a field. 21 is generalized uniserial if every primitive (left or right) ideal has a unique composition series. 21 is a UMFR algebra (an algebra with a unique minimal faithful representation) if 21 has only one faithful representation which is minimal with respect to being faithful. The notation used in this paper will be that of an e...

Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).

Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).