Related papers: P-Immune Sets with Holes Lack Self-Reducibility Pr…

This paper introduces and studies nil-reversible rings wherein we call a ring R nil-reversible if the left and right annihilators of every nilpotent element of R are equal. Reversible rings (and hence reduced rings) form a proper subclass…

We prove, by a straight construction, that the automorphism group of the measure algebra and the subgroup of the measure preserving ones cannot be isomorphic to the trivial automorphisms of P(N)/fin.

We study reductions that limit the extreme adaptivity of Turing reductions. In particular, we study reductions that make a rapid, structured progression through the set to which they are reducing: Each query is strictly longer (shorter)…

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free…

We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of…

We provide examples of contractible complexes which fail to have non-positive immersions and weak non-positive immersions, answering a conjecture of Wise in the negative.

We prove that the sumset {p^2+b^2+2^n: p is prime and b,n\in N} has positive lower density. We also construct a residue class with odd modulo, which contains no integer of the form p^2+b^2+2^n. And similar results are established for the…

We show that a large class of i.c.c., countable, discrete groups satisfying a weak negative curvature condition are not inner amenable. By recent work of Hull and Osin, our result recovers that mapping class groups and Out(F_n) are not…

We study the reduced Lefschetz module of the complex of p-radical and p-centric subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with…

We show that if $p_1,p_2$ are injective, integer polynomials that vanish at the origin, such that either both are of degree $1$ or both are of degree $2$ or higher, then double recurrence fails for non-commuting, mixing, zero entropy…

Let $A$ be a commutative Noetherian ring of characteristic $p>0$, such that $\dim(A)=d$. Let $P$ be a projective $A[T_1,...,T_n]$-module of rank $d$. We show that $P$ is cancellative if and only if $P/<T_1,...,T_n>P$ is cancellative. We…

We investigate issues surrounding an old question of Yates' as to the existence of a minimal Turing degree with no strong minimal cover, specifically with respect to the hyperimmune-free degrees.

Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with…

If $L$ is a relational language, then an $L$-structure ${\mathbb X}=\langle X,\bar \rho \rangle$ is reversible iff there is no interpretation $\bar \sigma \varsubsetneq \bar \rho$ such that the structures $\langle X,\bar \sigma \rangle$ and…

We prove that for any finite set A of real numbers its difference set D:=A-A has large product set and quotient set, namely, |DD|, |D/D| \gg |D|^{1+c}, where c>0 is an absolute constant. A similar result takes place in the prime field F_p…

p-jets of finite flat maps of schemes are generally neither finite nor flat. This phenomenon can be seen already in the case of p-isogenies of group schemes. However, for p-divisible groups, this pathology tends to disappear mod p "in the…

We investigate some properties of the $p$-elements of a profinite group $G$. We prove that if $p$ is odd and the probability that a randomly chosen element of $G$ is a $p$-element is positive, then $G$ contains an open prosolvable subgroup.…

We prove that a generic p.m.p. action of a countable amenable group $G$ has scaling entropy that can not be dominated by a given rate of growth. As a corollary, we obtain that there does not exist a topological action of $G$ for which the…

Let $G$ be a finite $p$-group.