Related papers: On free elementary ZpCp lattices

A complete description of subgroups in the general linear group over a semilocal ring containing the group of diagonal matrices was obtained by Z.I.Borewicz and N.A.Vavilov. It is shown in the present paper that a similar description holds…

Let $\mathcal O_p$ denote the characteristic $p>0$ version of the ordinary category $\mathcal O$ for a semisimple complex Lie algebra. In this paper we give some (formal) character formulas in $\mathcal O_p$. First we concentrate on the…

Let $N$ be a positive integer and let $f$ be a meromorphic modular function of level $N$ with rational Fourier coefficients. For a prime $p$, define a function $f_p$ on the complex upper half-plane $\mathbb{H}$ by \begin{equation*}…

We show that for every positive p, the L_p-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. random variables, whose moduli have a nondegenerate distribution with the p-norm one, is comparable to the…

We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of…

We show that the free module of infinite rank $R^{(\kappa)}$ purely embeds every $\kappa$-generated flat left $R$-module iff $R$ is left perfect. Using a Bass module corresponding to a descending chain of principal right ideals, we…

We show that the set of all (unimodular and non-unimodular) free cyclic submodules of T^2, where T is the ring of ternions over a commutative field, admits a point model in terms of a smooth algebraic variety.

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous article, we gave a necessary and sufficient condition for X to be free of given rank d…

We show that every $PD_3$-complex $P$ bounds a $PD_4$-pair $(Z,P)$. If $P$ is orientable we may assume that $\pi_1(Z)=1$. We show also that if $P$ has a manifold 1-skeleton then it is homotopy equivalent to a closed 3-manifold, and that if…

For each integer partition $\mathbf{q}$ with $d$ parts, we denote by $\Delta_{(1,\mathbf{q})}$ the lattice simplex obtained as the convex hull in $\mathbb{R}^d$ of the standard basis vectors along with the vector $-\mathbf{q}$. For…

A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral…

In this article, we study rational matrix representations of VZ $p$-groups ($p$ is any prime). Utilizing our findings on VZ $p$-groups, we explicitly obtain all inequivalent irreducible rational matrix representations of all $p$-groups of…

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…

We study the fundamental group of the $p$-subgroup complex of a finite group $G$. We show first that $\pi_1(A_3(A_{10}))$ is not a free group (here $A_{10}$ is the alternating group on $10$ letters). This is the first concrete example in…

We consider a variation of Construction A of lattices from linear codes based on two classes of number fields, totally real and CM Galois number fields. We propose a generic construction with explicit generator and Gram matrices, then focus…

We study the rational torsion subgroup of the modular Jacobian $J_0(N)$ for $N$ a square-free integer. We give a new proof of a result of Ohta on a generalization of Ogg's conjecture: for a prime number $p \nmid 6N$, the $p$-primary part of…

Let A be a del Pezzo order on the projective plane over the field of complex numbers. We prove that every torsion-free A-module of rank one can be deformed into a locally free A-module of rank one.

The main result of this article establishes the free analog of Grothendieck's Theorem on bijective polynomial mappings of $\mathbb{C}^g$. Namely, we show if $p$ is a polynomial mapping in $g$ freely non-commuting variables sending…

We prove a sharp upper bound on the number of distinct columns of a totally unimodular matrix with column sums $1$ improving upon Heller's classical bound. The proof uses Seymour's decomposition theorem. Such matrices are closely related to…

For every prime $p$ it is shown that a wide class of HNN extensions of free abelian groups admit faithful representation by finite $p$-automata.