The of rings with many units
The -groups of -rings. Part I. Construction of the logarithmic invariant
The -groups of -rings. Part II. Invertibility of the logarithmic map
The -zero-divisor hypergraph of a commutative ring.
The Kadison problem on a class of commutative Banach algebras with closed cone
The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra that all of its squares are positive and satisfying the following property: Every continuous bilinear map from into an arbitrary Banach space such that whenever , satisfies the condition for all .
The Koszul Algebra of a Codimension 2 Embedding.
The Krull-Schmidt theorem for categories of finitely generated modules over valuation domains.
The Krull-Schmidt theorem for Henselian rings.
The last coefficient of the Samuel polynomial
The last coefficient of the Samuel polynomial
The lattice of radical filters of a commutative Noetherian ring
The Lazarsfeld-Rao problem for Buchsbaum curves
The Lê varieties, I.
The least solution for the polynomial interpolation problem.
The Lifting of determinal prime ideals.
The linear syzygy graph of a monomial ideal and linear resolutions
For each squarefree monomial ideal , we associate a simple finite graph by using the first linear syzygies of . The nodes of are the generators of , and two vertices and are adjacent if there exist variables such that . In the cases, where is a cycle or a tree, we show that has a linear resolution if and only if has linear quotients and if and only if is variable-decomposable. In addition, with the same assumption on , we characterize all squarefree monomial ideals with a...
The local lifting problem for actions of finite groups on curves
Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB obstruction...
The logic of Rumely's local-global principle.
The L-Theory of Laurent extensions and genus 0 function fields.
The maximal regular ideal of some commutative rings
In 1950 in volume 1 of Proc. Amer. Math. Soc., B. Brown and N. McCoy showed that every (not necessarily commutative) ring has an ideal consisting of elements for which there is an such that , and maximal with respect to this property. Considering only the case when is commutative and has an identity element, it is often not easy to determine when is not just the zero ideal. We determine when this happens in a number of cases: Namely when at least one of or has a von Neumann inverse,...