An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possible Hilbert functions of Artinian Gorenstein algebras with the Weak Lefschetz Property, a property shared by most Artinian Gorenstein algebras. Starting with an arbitrary SI-sequence, we construct a reduced, arithmeti...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

It is unknown if an Artinian level O-sequence of codimension 3 and type r (≥ 2) is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra A of codimension 3 has the Hilbert function H : h0 h1 · · · hd−1 hd · · · hd }...

One of the fundamental problems in the study of moduli spaces is to give an intrinsic characterisation of representable functors of schemes, or of functors that are quotients of representable ones of some sort. Such questions are in general hard, leading naturally to geometry of algebraic stacks and spaces (see [1, 3]). On the other hand, in infinitesimal deformation theory a classical criterio...

This paper investigates the class of rings in which every nn-absorbing ideal is a prime ideal, called nn-AB ring, where nn positive integer. We give characterization an ring. Next, for ring RR, we study concept Ω(R)={ωR(I);I proper R},Ω(R)={ωR(I);I R}, ωR(I)=min{n;I n-absorbing R}ωR(I)=min{n;I R}. show that if RR Artinian or Prüfer domain, then Ω(R)∩NΩ(R)∩N does not have any gaps (i.e., wheneve...

We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. use this to give new version theorem Hellus characterizing set-theoretic complete intersections in terms local cohomology modules. also define quasi-cyclic as increasing unions cyclic modules, show at least two are quasi-cyclic. then focus our attention on...

The paper deals with ring extensions $$R\subseteq S$$ and their lattices [R, S] of subextensions is mainly devoted to FCP (extensions whose are Artinian Noetherian). object the introduction study elements that split in some sense extensions. reason why this splitting was used earlier without common nature being recognized. There favorable cases allowing build splitters, when we dealing $${\math...