Semi-Baer modules

2015 ◽  
Vol 14 (10) ◽  
pp. 1550145 ◽  
Author(s):  
B. N. Waphare ◽  
Anil Khairnar
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Group Ring ◽  
Semi Group ◽  
Multiplicative Order ◽  
Order Of An Element ◽  
Baer Modules ◽  
Polynomial Extensions

In this paper, we introduce the concepts of semi-Baer, semi-quasi Baer, semi-p.q. Baer and semi-p.p. modules as a generalization of Baer, quasi Baer, p.q. Baer and p.p. modules respectively. To define these concepts, we introduce concepts of multiplicative order of an element and a multiplicatively finite element in rings. Further, we characterize these concepts in modules over reduced rings. Also, it is proved that semi-Baer and semi-quasi Baer properties are preserved by polynomial extensions and power series extensions of modules. It is proved that for a ring R and a monoid G, if the semi group ring RG is semi-Baer (semi-quasi Baer) then so is R.

Homology of the Fermat Tower and Universal Measures for Jacobi Sums

2016 ◽  
Vol 59 (3) ◽  
pp. 624-640
Author(s):  
Noriyuki Otsubo
Keyword(s):  
Power Series ◽  
Group Ring ◽  
Simple Proof ◽  
Homology Group ◽  
Interpolation Property ◽  
Cyclic Module ◽  
Precise Description ◽  
Fermat Curve ◽  
Jacobi Sums ◽  
Definition Of

AbstractWe give a precise description of the homology group of the Fermat curve as a cyclic module over a group ring. As an application, we prove the freeness of the profinite homology of the Fermat tower. This allows us to define measures, an equivalent of Anderson’s adelic beta functions, in a manner similar to Ihara’s definition of ℓ-adic universal power series for Jacobi sums. We give a simple proof of the interpolation property using a motivic decomposition of the Fermat curve.

scholarly journals A Gorenstein numerical semi-group ring having a transcendental series of Betti numbers

2015 ◽  
Vol 219 (3) ◽  
pp. 591-621
Author(s):  
Clas Löfwall ◽  
Samuel Lundqvist ◽  
Jan-Erik Roos
Keyword(s):  
Group Ring ◽  
Betti Numbers ◽  
Semi Group

A FINITE ELEMENT PLATE FORMULATION FOR THE ACOUSTICAL INVESTIGATION OF THIN AIR LAYERS

2013 ◽  
Vol 21 (04) ◽  
pp. 1350014 ◽  
Author(s):  
PING RONG ◽  
OTTO VON ESTORFF ◽  
LORIS NAGLER ◽  
MARTIN SCHANZ
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Transmission Loss ◽  
Fluid Layer ◽  
Single Layer ◽  
Shell Element ◽  
Thin Plates ◽  
Element Analysis ◽  
Shell Elements ◽  
Double Wall

Double wall systems consisting of thin plates separated by an air gap are common light-weighted wall structures with high transmission loss. Generally, these plate-like structures are modeled in a finite element analysis with shell elements and volume elements for the air (fluid) layer. An alternative approach is presented in this paper, using shell elements for the air layer as well. First, the element stiffness matrix is obtained by removing the thickness dependence of the variational form of the Helmholtz equation by use of a power series. Second, the coupling between the acoustical shell element and the elastic structure is described. To verify the new shell element, a simple double wall system is considered. Comparing the predicted sound field with the results from a commercial FE software (with a single layer of volume elements) a very good agreement is observed. At the same time, employing the new elements with a third-order power series (4 DOFs per node), the calculation time is reduced.

On Proving the Absence of Zero-Divisors for Semi-Group Rings

1961 ◽  
Vol 4 (3) ◽  
pp. 225-231 ◽  
Author(s):  
Bernhard Banaschewski
Keyword(s):  
Characteristic Function ◽  
Group Ring ◽  
Neutral Element ◽  
Group Rings ◽  
Semi Group ◽  
Zero Divisors

For any semi-group S and any ring Λ with unit 1 (always taken to be distinct from 0, the neutral element of Λ under addition) there is known to exist a ring Λ[S] ⊇S which is a A-bimodule such that (i) S is a sub semi-group of the multiplicative semi-group of Λ[S], (ii) λs = sλ, (iii) λ(st) = (λs)t = s(λt) ( s, t ∊ S and λ∊Λ) and (iv) Sis a Λ -basis of Λ[S]. This ring is uniquely determined by these conditions and is usually called the semi-group ring of S over Λ. It may be described explicitly as consisting of the functions f: S → Λ which vanish at all but finitely many places, with functional addition (f+g) (s) = f(s) + g(s) and convolution (fg) (s) = Σf(u) g(v) (uv = s) as the ring operations, the functional A-bimodule operations (λf) (s) = λf(s) and (fλ) (s) - f(s)λ, and each s ∊ S identified with the characteristic function of { s} with values in Λ.

scholarly journals Almost Krull rings

1986 ◽  
Vol 41 (2) ◽  
pp. 275-285
Author(s):  
E. Jespers ◽  
P. Wauters
Keyword(s):  
Group Ring ◽  
Polynomial Identity ◽  
Chain Condition ◽  
Polynomial Rings ◽  
Semi Group ◽  
Cyclic Subgroups ◽  
Skew Polynomial Rings ◽  
Krull Domain ◽  
Skew Polynomial ◽  
Ascending Chain Condition

AbstractThe notion of an almost Krull domain is extended to rings satisfying a polynomial identity. Some general structural results are obtained. We also prove that skew polynomial rings R [ X, σ] remain almost Krull if R is an almost Krull ring. Finally, we study when semigroup ring R[S] are almost Krull rings, in the case when the group of quotients of S has the ascending chain condition on cyclic subgroups. An example is included to show that the general (semi-) group ring case is much more difficult to deal with.

scholarly journals STRONGLY CLEAN POWER SERIES RINGS

2007 ◽  
Vol 50 (1) ◽  
pp. 73-85 ◽  
Author(s):  
Jianlong Chen ◽  
Yiqiang Zhou
Keyword(s):  
Finite Group ◽  
Power Series ◽  
Group Ring ◽  
Regular Ring ◽  
Locally Finite Group ◽  
Locally Finite ◽  
Regular Elements ◽  
Strongly Regular ◽  
Power Series Rings

AbstractAn element $a$ in a ring $R$ with identity is called strongly clean if it is the sum of an idempotent and a unit that commute. And $a\in R$ is called strongly $\pi$-regular if both chains $aR\supseteq a^2R\supseteq\cdots$ and $Ra\supseteq Ra^2\supseteq\cdots$ terminate. A ring $R$ is called strongly clean (respectively, strongly $\pi$-regular) if every element of $R$ is strongly clean (respectively, strongly $\pi$-regular). Strongly $\pi$-regular elements of a ring are all strongly clean. Let $\sigma$ be an endomorphism of $R$. It is proved that for $\varSigma r_ix^i\in R[[x,\sigma]]$, if $r_0$ or $1-r_0$ is strongly $\pi$-regular in $R$, then $\varSigma r_ix^i$ is strongly clean in $R[[x,\sigma]]$. In particular, if $R$ is strongly $\pi$-regular, then $R[[x,\sigma]]$ is strongly clean. It is also proved that if $R$ is a strongly $\pi$-regular ring, then $R[x,\sigma]/(x^n)$ is strongly clean for all $n\ge1$ and that the group ring of a locally finite group over a strongly regular or commutative strongly $\pi$-regular ring is strongly clean.

A Novel Power Series Method for the Analysis of an Offshore Mooring Line

2021 ◽  
Author(s):  
Kabutakapua Kakanda ◽  
Zhaolong Han ◽  
Bao Yan ◽  
Narakorn Srinil ◽  
Dai Zhou
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Initial Conditions ◽  
Dynamic Strain ◽  
Mooring Line ◽  
Series Method ◽  
Lumped Mass ◽  
Mooring Lines ◽  
Bivariate Polynomials ◽  
Power Series Method

Abstract The mechanics of offshore mooring lines are described by a set of nonlinear equations of motion which have typically been solved through a numerical finite element or finite difference method (FEM or FDM), and through the lumped mass method (LMM). The mooring line nonlinearities are associated with the distributed drag forces depending on the relative velocities of the environmental flow and the structure, as well as the axial dynamic strain-displacement relationship given by the geometric compatibility condition of the flexible mooring line. In this study, a semi analytical-numerical novel approach based on the power series method (PSM) is presented and applied to the analysis of offshore mooring lines for renewable energy and oil and gas applications. This PSM enables the construction of analytical solutions for ordinary and partial differential equations (ODEs and PDEs) by using series of polynomials whose coefficients are determined, depending on initial and boundary conditions. We introduce the mooring spatial response as a vector in the Lagrangian coordinate, whose components are infinite bivariate polynomials. For case studies, a two-dimensional mooring line with fixed-fixed ends and subject to nonlinear drag, buoyancy and gravity forces is considered. The introduced boundary and initial conditions enable the analysis of an equilibrium or steady-state of a catenary-like mooring line configuration with variable slenderness and flexibility. Polynomials’ coefficients computation is performed with the aid of a MATLAB package. Numerical results of mooring line configurations and resultant tensions are presented for deep-water applications, and compared with those obtained from a semi-analytical and finite element model. The PSM applied to the mooring line in the present study is efficient and more computationally robust than traditional numerical methods. The PSM can be directly applied to the dynamic analysis of mooring lines.

Improved Finite Element Model for Lateral Stability Analysis of Axially Functionally Graded Nonprismatic I-beams

2019 ◽  
Vol 19 (09) ◽  
pp. 1950108 ◽  
Author(s):  
Masoumeh Soltani ◽  
Behrouz Asgarian ◽  
Foudil Mohri
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Material Properties ◽  
Volume Fraction ◽  
Weak Form ◽  
Element Model ◽  
Functionally Graded ◽  
Element Formulation ◽  
Lateral Buckling ◽  
Simply Supported

This paper investigates the lateral buckling of simply supported nonprismatic I-beams with axially varying materials by a novel finite element formulation. The material properties of the beam are assumed to vary continuously through the axis according to the volume fraction of the constituent materials based on an exponential or a power law. The torsion governing equilibrium equation of the simply supported beam with free warping is numerically solved by employing the power series approximation. To this end, all the mechanical properties and displacement components are expanded in terms of the power series to a known degree. Then the shape functions are obtained by representing the deformation shape of the axially functionally graded (AFG) web and/or flanges tapered thin-walled beam in a power series form. At the end, new [Formula: see text] elastic and buckling stiffness matrices are exactly determined from the weak form expression of the governing equation. Three comprehensive examples each of axially nonhomogeneous and homogeneous tapered beams with doubly symmetric I-sections are presented to evaluate the effects of different parameters such as axial variation of material properties, tapering ratio and load height parameters on the lateral buckling strength of the beam. The numerical outcomes of this paper can serve as a benchmark for future studies on lateral-torsional critical loads of AFG beams with varying I-sections.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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