Let R be a standard graded algebra over field k and I homogeneous ideal of R. We study the question whether there is constant c such that Soc(Hmj(R/It))<−ct=0 for all t≥1 variation this question. also draw connection between notion gauge-boundedness in prime characteristic.

Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings. 0. Introduction. We study affine rings (i.e., rings finitely generated as algebras ov...

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in...

In this paper, we study the relationships between graphs and prime spectrum of unitary commutative rings. It is shown that a graph G equipped with G-right topology satisfies some spectral properties. particular give necessarily sufficient condition to obtain graph.

For a commutative Hopf algebra A over Z/p, where p is a prime integer, we define the Steenrod operations P i in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group S n and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations. 1. Introduction. For any prime p, the mod p Steenrod...

In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...

We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the non...

Let X be a finite, n-dimensional, r-connected CW complex. We prove the following theorem: If p ≥ n/r is an odd prime, then the loop space homology Bockstein spectral sequence modulo p is a spectral sequence of universal enveloping algebras over differential graded Lie algebras.