Symmetric modules over their endomorphism rings

Let R be an arbitrary ring with identity and M a right R-module with S=EndR(M). In this paper, we study right R-modules M having the property for f,g∈EndR(M) and for m∈M, the condition fgm=0 implies gfm=0. We prove that some results of symmetric rings can be extended to symmetric modules for this general setting

Symmetric modules over their endomorphism rings

Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we study right R-modules M having the property for f, g ∈ EndR(M) and for m ∈ M, the condition fgm = 0 implies gfm = 0. We prove that some results of symmetric rings can be extended to symmetric modules for this general setting. © Journal “Algebra and Discrete Mathematics”

Generalized symmetric rings

In this paper, we introduce a class of rings which is a generalization of symmetric rings. Let R be a ring with identity. A ring R is called central symmetric if for any a, b,c∈R, abc=0 implies bac belongs to the center of R. Since every symmetric ring is central symmetric, we study sufficient conditions for central symmetric rings to be symmetric. We prove that some results of symmetric rings can be extended to central symmetric rings for this general settings. We show that every central reduced ring is central symmetric, every central symmetric ring is central reversible, central semmicommutative, 2-primal, abelian and so directly finite. It is proven that the polynomial ring R[x] is central symmetric if and only if the Laurent polynomial ring R[x,x−1] is central symmetric. Among others, it is shown that for a right principally projective ring R, R is central symmetric if and only if R[x]/(xn) is central Armendariz, where n≥2 is a natural number and (xn) is the ideal generated by x

Rain water chemistry in Ankara, Turkey

Samples of rain water were collected in Ankara for the period between September 1989 and May 1990, by using wet-only sampler. Concentrations of major cations (H+, Na+, K+, Ca2+ and NH4+) and major anions (Cl-, NO3- and SO42-) were determined for the first time in Turkey. The rain water was not acidic owing to high concentrations of alkaline soil particles in the atmosphere. However, the concentrations of acid forming ions, such as SO42- and NO3-, were higher than the concentrations expected in a typical urban atmosphere. Most of the SO42- in rain water was in the form of CaSO4. Rain-aerosol coupling were examined by simultaneous sampling of aerosols with rain. The ions most efficiently scavenged from the atmosphere were found to be SO42- and Ca2+. (C) 1996 Elsevier Science Lt

A generalization of reduced rings

Let R be a ring with identity. We introduce a class of rings which is a generalization of reduced rings. A ring R is called central rigid if for any a, b ? R, a2b = 0 implies ab belongs to the center of R. Since every reduced ring is central rigid, we study sufficient conditions for central rigid rings to be reduced. We prove that some results of reduced rings can be extended to central rigid rings for this general setting, in particular, it is shown that every reduced ring is central rigid, every central rigid ring is central reversible, central semicommutative, 2-primal, abelian and so directly finite

A generalization of reversible rings

WOS: 000344830500006In this paper, we introduce a class of rings which is a generalization of reversible rings. Let R be a ring with identity. A ring R is called central reversible if for any a,b is an element of R, ab=0 implies ba belongs to the center of R. Since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. We prove that some results of reversible rings can be extended to central reversible rings for these general settings

Strongly Large Module Extensions

In this paper, we introduce strongly large submodules and investigate their properties. A submodule N of a right R-module M is said to be strongly large in case for any m is an element of M, s is an element of R with ms not equal 0 there exists an r is an element of R such that mr is an element of N and mrs not equal 0. In this note, we also define and study strongly large closed submodules and strongly large complement submodules.WoSScopu

Stabilization parameters and smagorinsky turbulence model

For the streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations for flow problems, we present in this paper a comparative study of the stabilization parameters defined in different ways. The stabilization parameters are closely related to the local length scales ("element length"), and our comparisons include parameters defined based on the element-level matrices and vectors, some earlier definitions of element lengths, and extensions of these to higher-order elements. We also compare the numerical viscosities generated by these stabilized formulations with the eddy viscosity associated with a Smagorinsky turbulence model that is based on element length scales