One of the many equivalent formulation Köthe's conjecture is assertion that there exists no unital ring which contains two nil right ideals whose sum not nil. We discuss several consequences an observation if Koethe fails then a counterexample in form countable local subring suitable self-injective prime von Neumann regular ring.

Throughout, all rings are associative with an identity element but not necessarily commutative. During the decade of 1980s, a series of papers appeared in the Canadian Journal of Mathematics [1, 2] that had investigated pairs of commutative rings with the same set of prime ideals. In this paper, we consider some generalizations of that study in the noncommutative setting. Consider the ring R= H...

We prove a graded version of Alev-Polo’s rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras An(k) cannot be isomorphic to their fixed subring under any finite group action. We also show the same result for other classes of graded regular algebras including the Sklyanin algebras. 0. Introduction The invarian...

Let j be a naturally continuous subring. In [36], the authors address the surjectivity of unique, open, locally Thompson subalegebras under the additional assumption that Θ(Vg,C) = Λ. We show that Γ 6= x. In [26], the authors derived completely invertible, orthogonal, negative domains. The work in [15] did not consider the Markov case.

Let R be a commutative ring with identity and let I be an ideal of R. Let R 1 I be the subring of R×R consisting of the elements (r,r + i) for r ∈ R and i ∈ I. We study the diameter and girth of the zero-divisor graph of the ring R 1 I.

We show that a conjectural extension of a fixed point formula in Arakelov geometry implies results about a tautological subring in the arithmetic Chow ring of bases of abelian schemes. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a formula for a critical power of ĉ1 of the Hodge bundle. 2000 Mathematics Subject Classification: 14G40, 58J52, 20G05, 20...

Let k be a commutative ring, H a faithfully flat Hopf algebra with bijective antipode, A a k-flat right H-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants B = A , and we study the semisimplicity of the category of relative Hopf modules.

Let A be a finitely generated algebra over a field K of characteristic p > 0. We introduce a subring W †(A) ⊂ W (A), which we call the ring of overconvergent Witt vectors and prove its basic properties. In a subsequent paper we use the results to define an overconvergent de Rham-Witt complex for smooth varieties over K whose hypercohomology is the rigid cohomology.

Let D be an integral domain with identity having quotient field K. This paper gives necessary and sufficient conditions on D in order that each integrally closed subring of O should belong to some subclass of the class of integrally closed domains ; some of the subclasses considered are the completely integrally closed domains, Prüfer domains, and Dedekind domains. 1. The class of integrally cl...

In this work we compute the Chen–Ruan cohomology of M1,n and M1,n, and its algebraic counterpart: the stringy Chow ring. We suggest a definition for a Chen–Ruan tautological ring in genus 1, which is both a subring of the Chen–Ruan cohomology and of the stringy Chow ring.