‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

Let be a ring. We use mod (resp. mod ) to denote the category of finitely generated left -modules (resp. right -modules). We always assume that and are Artinian algebras and is a faithfully balanced self-orthogonal bimodule, that is, satisfies the following conditions: (1) is in mod and is in mod ; (2) the natural maps → End op and → End are isomorphisms; (3) Ext = 0 and Ext = 0 for any i ≥ 1. ...

in this paper, an extension of record models, well known as k-records, is considered. bayesian estimation as well as prediction based on k-records are presented when the underlying distribution is assumed to have a general form. the proposed procedure is applied to the exponential, weibull and pareto models in one parameter case. also, the two-parameter exponential distribution, when both param...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

Let k be a finite extension of Qp and Ek be the set of the extensions of degree p over k whose normal closure is a p-extension. For a fixed discriminant, we show how many extensions there are in EQp with such discriminant, and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalize...

Let k be a number field. A natural question is: Does k admit an infinite unramified extension? The answer is no, if the root discriminant of k is less than Odlyzko’s bounds. The answer is yes, if k fails the test of Golod-Shafarevic for a prime number p. In that case, we know that there exists an infinite unramified p-extension L over k. But generally it is fairly difficult to determin whether ...