let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing xn − λ over Fq2 is given, where λ is a unit in Fq2 . Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over Fq2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dua...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

In arXiv:0709.0483 Günther and Samsonov outline a “generalization” of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be “capable to produce effects beyond those of standard Hermitian quantum mechanics.” We give a simple physical interpretation of Hermiticity and discuss in detail the shortcomings of the above-mentioned composi...

The purpose of this paper is to study certain notions metric positivity called “minimal extension property” for the lowest nonzero piece in Hodge filtration a module. Let X be complex manifold and let $$\mathcal {M}$$ polarized pure module on with strict support X. $$F_p\mathcal smallest filtration. Assume that smooth outside closed analytic subset Z $$j:X\setminus \hookrightarrow X$$ open embe...

We call a positive definite even Hermitian lattice even universal if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields Q( √ −m) for all m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermitian lattices. And we apply our r...

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...