We propose a recipe for constructing fiducial vector symmetric informationally complete positive operator valued measure (SIC-POVM) in complex Hilbert space of dimension the form d = n 2 + 3, focusing on prime dimensions p. Such structures are shown to exist 13 this kind, highest being p 19 603. The real quadratic base field K (in standard SIC-POVM terminology) attached such has fundamental uni...

In this paper, we introduce a new class $\mathcal{R}^{\alpha}_{m}(h)$ of functions $F=f\ast\psi$, defined in the open unit disc $E$ with $F(0)=F^{\prime}(0)-1=0$ and satisfying condition \begin{equation*} F^{\prime}(z)+\alpha zF^{\prime\prime}(z)=\left(\frac{m}{4}+\frac{1}{2}\right)p_{_{1}}(z)-\left(\frac{m}{4}-\frac{1}{2}\right)p_{_{2}}(z), \end{equation*} for $\alpha\geq0,\,m\geq2$ $p_{_{i}}\...

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

The purpose of this paper is to introduce a new concept in module M over ring R, called e∗-essential submodule, which generalization an essential submodule. We will some examples and properties about such that, what the inverse image intersection submodules direct sum submodules. show relationship between submodule Noetherian R-module. Also we define e∗-closed with

The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...

It has been observed by different authors that QTAG-modules behave very much like torsion abelian groups. In this paper, in section 3, we characterize quasi-essential submodules (Theorem 3.9) and further find a characterization for an h-pure submodule to be a direct summand (Theorem 3.11). In section 4, we obtained a necessary and sufficient condition for a submodule to be contained in a minima...

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable ...

Proposition 1. Assume that r = n − m > 1 and that the first nonvanishing Fitting ideal of M has grade r + 1. Then the following conditions are equivalent. (1) There is a χ ∈ M∗ = HomR(M,R) such that the ideal Imχ has grade r + 1. (2) There exists a submodule U of M with the following properties: (i) rankU = r − 1; (ii) U is reflexive, orientable, and Up is a free direct summand of Mp for all pr...

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

and Applied Analysis 3 In 15 the asymptotic behavior of 1.1 was studied and it was proven the existence of a global attractor for the semigroup associated to 1.1 , that is, the semigroup of operators defined as S t : u0 ∈ H −→ u t ∈ H, 1.4 The main tool in proving the existence of a global attractor is to show the existence of an absorbing set inH2 I see Theorem 1.1 in 1 . Theorem 1.1 see 15 . ...