The paper studies the following question: Given a ring R, when does the zero-divisor graph (R) have a regular endomorphism monoid? We prove if R contains at least one nontrivial idempotent, then (R) has a regular endomorphism monoid if and only if R is isomorphic to one of the following rings: Z2 × Z2 × Z2; Z2 × Z4; Z2 × (Z2[x]/(x)); F1 × F2, where F1, F2 are fields. In addition, we determine a...

We show that cohopfian modules with finite exchange have countable exchange. In particular, a module whose endomorphism ring is Dedekind-finite and π-regular has the countable exchange property. We also show that a module whose en-domorphism ring is Dedekind-finite and regular has full exchange. Finally, working modulo the Jacobson radical, we prove that any module with the (C 2) property and a...

Abstract. Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the needlet kernel for nonparametric regression problems whose predictor variables are defined on a sphere. Due to the localization property in the frequenc...

Let R be a local ring of positive characteristic and X complex with nonzero finitely generated homology finite injective dimension. We prove that if the derived base change via Frobenius (or more generally, contracting) endomorphism has dimension then is Gorenstein. In particular, we give an affirmative answer to question by Falahola Marley [7, Question 3.9].

For V a vector space over a field, or more generally, over a division ring, it is well-known that every x ∈ End(V ) has an inner inverse; that is, that there exists y ∈ End(V ) satisfying xyx = x. We show here that a large class of such x have inner inverses y that satisfy with x an infinite family of additional monoid relations, making the monoid generated by x and y what is known as an invers...

Generalized conjugation is the action of a group on its underlying set given by (g, x) 7→ φ(g)xg, where φ : G → G is some fixed endomorphism. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if φ has a nontrivial kernel or if it is an inner automorphism, and we give a construction that allows a part...

K: a global function field of characteristicp # 0 E a fixed algebraic closure of K 00: a distinguished place of K A: the ring of functions in K regular away from cx> F,: a finite field which is an A-algebra VI the A-characteristic of F, (this means that the prime ideal pt, of v is the kernel of the structure morphism A + F4) 4 : a Drinfeld A-module over F, of rank d 7~: The Frobenius endomorphi...

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with homomorphisms G→ H. (Precise statement in §1.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of G itself, is...

Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...