Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...

This article consists of a collection of open problems in commutative algebra. The collection covers a wide range of topics from both Noetherian and non-Noetherian ring theory and exhibits a variety of research approaches, including the use of homological algebra, ring theoretic methods, and star and semistar operation techniques. The problems were contributed by the authors and editors of this...

An expression in terms of (cyclotomic) harmonic sums can be simplified by the quasi-shuffle algebra in terms of the so-called basis sums. By construction, these sums are algebraically independent within the quasi-shuffle algebra. In this article we show that the basis sums can be represented within a tower of difference ring extensions where the constants remain unchanged. This property enables...

The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...

We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated.

We consider random hermitian matrices in which distant abovediagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has algebraic Stieltjes transform by an argument based on dimension theory of noetherian local rings.

The ring structure of Lian-Zuckerman states for (q, p) minimal models coupled to gravity is shown to beR = R0⊗C[w,w] where R0 is the ring of ghost number zero operators generated by two elements and w is an operator of ghost number −1. Some examples are discussed in detail. For these models the currents are also discussed and their algebra is shown to contain the Virasoro algebra. † Address aft...

In this paper we consider several constructions which from a given B-product ∗B lead to another one ∗̃B . We shall be interested in finding what algebraic properties of the ring RB = 〈CN, +, ∗B 〉 are shared also by the ring RB̃ = 〈C N, +, ∗B 〉. In particular, for some constructions the rings RB and RB̃ will be isomorphic and therefore have the same algebraic properties. §

Abstract Let D be a finite-dimensional division algebra over its center and R = [ t ; ? , ? ] skew polynomial ring. Under certain assumptions on the ring of central quotients ( ) { f / g | ? ], C ])} is simple with reduced norm N . We calculate for some polynomials investigate when how reducibility reflects

One of the basic questions in number theory is to determine semi-simple l-adic representations of the absolute Galois group of a number field F . In case of abelian representations, a satisfactory answer is known for compatible system of l-adic representations, and these types of abelian representations are obtained from algebraic Hecke characters. In this paper, we discuss the question for two...