in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

We prove the following. Theorem. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groups Gv having asdimGv ≤ n for all vertices v. Then asdimπ ≤ n + 1. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.

Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.

Let T be the quasi-nilpotent DT-operator. By use of Voiculescu’s amalgamated R-transform we compute the momets of (T −λ1)∗(T − λ1) where λ ∈ C, and the Brown-measure of T + √ Y , where Y is a circular element ∗-free from T for > 0. Moreover we give a new proof of Śniady’s formula for the moments τ(((T ∗)kT )) for k, n ∈ N.

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...