On Skew Power-serieswise nil-Armendariz Rings

For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.

SELF-DUAL PERMUTATION CODES OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.

Principal Quasi-Baerness of Rings of Generalized Power Series

Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.

PS-modules over Rings of Generalized Power Series

Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.

Principal Quasi-Baerness of Rings of Skew Generalized Power Series

Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

Differential Inverse Power Series Rings with Quasi-Armendariz-like Condition

A generalization of semiprime rings and right p.q.-Baer rings,which we call quasi-Armendariz rings of differential inverse power series type(or simply,DTPS-quasi-Armendariz),is introduced and studied.It is shown that the DTPS-quasi-Armendariz rings are closed under direct sums,upper triangular matrix rings,full matrix rings and Morita invariance.Various classes of non-semiprime DTPS-quasi-Armendariz rings are provided,and a number of properties of this generalization are established.Some characterizations for the differential inverse power series ring R[[x^-1;δ]]to be quasi-Baer,generalized quasi-Baer,primary,nilary,reflexive,ideal-symmetric and left AIP are conncluded,whereδis a derivation on the ring R.Finally,miscellaneous examples to illustrate and delimit the theory are given.

Principal Quasi-Baerness of Skew Power Series Rings

Let R be a ring such that all left semicentral idempotents axe central and α a weakly rigid endomorphism of R. It is shown that the skew power series ring R[[x; α]] is right p.q.Baer if and only if R is right p.q.Baer and any countable family of idempotents in R has a generalized join in I(R), where I(R) is the set of all idempotents of R.

幂级数π-Armendariz环

引入幂级数π-Armendariz环的概念,研究了幂级数π-Armendariz环的扩张,证明了如果环R是具有幂零有界指数的NI环,且为α-容许环,则R[x;α]是幂级数π-Armendariz环.同时讨论了幂级数环的幂零p.p.性和弱zip性.

幂级数J-Armendariz环

引入幂级数J-Armendariz环的概念,进一步扩展幂级数Armendariz环的研究。证明了:(1)设T=(R 0 M S)是一个形式三角矩阵环,则T是幂级数J-Armendariz环当且仅当R和S都是是幂级数J-Armendariz环;(2)设{R_αα∈Λ}是一族环,则直积∏α∈ΛR_α是幂级数J-Armendariz环当且仅当每一个环R_α都是幂级数J-Armendariz环;(3)如果环R是幂级数J-Armendariz环,满足J(R)[x]=J(R[x]),则R[x]是幂级数J-Armendariz环。

多级谐振充电的Marx脉冲源研究

Marx发生器是一种经典的脉冲功率发生装置。为了更好地满足高电压、双极性高效率等实际使用需求,文中提出了多级谐振充电的Marx脉冲源,即利用串联谐振充电源与串心磁环变压器对Marx脉冲发生器分组充电。搭建两类对称结构多级谐振充电的Marx脉冲发生器并验证其性能,包括可变极性的单极性发生器和双极性脉冲发生器。电路由一组正极性的3路8级Marx和一组负极性的3路8级Marx组成,共48级。实验结果表明,可变极性的单极性Marx发生器可产生正极性或负极性电压幅值为30 kV的脉冲,双极性发生器可向空载和50 kΩ的阻性负载输出±10 kV的电压脉冲。通过FPGA(Field Program Gate Array)的信号控制可以将重复频率控制在1 Hz~1 kHz范围内调节,脉宽可在1~200μs范围内调节,脉冲前后沿为50 ns以内。正、负脉冲之间的弛豫时间为0.2~200.0μs。

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].

Morita Duality for the Rings of Generalized Power Series

Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.

PP-Rings of Generalized Power Series

As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and （S.≤） a strictly totally ordered monoid. We prove that （1） the ring [[R(S.≤]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B（R） （the set of all idempotents of R） has a least upper bound in B（R）. and （2） if （S. ≤） also satisfies the condition that 0≤s for any s∈S, then the ring [[R(S.≤]] is weakly PP if and only if R is weakly PP.

ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS

Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.

Principal Quasi-Baerness of Formal Power Series Rings

Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.

On Pseudo Weakly Clean Rings

A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.

On the Cozero-Divisor Graphs of Commutative Rings

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.

Nonnil-Noetherian Rings and Formal Power Series

Let A be a commutative ring with unit.We characterize when A is nonnil-Noetherian in terms of the quotient ring A/Nil(A)and in terms of the power series ring A[[X]].

A Note on z-Ideals and z°-Ideals of the Formal Power Series Rings and Polynomial Rings in an Infinite Set of Indeterminates

Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation bet ween the z-ideals of A and t hose of the formal power series rings in an infinite set of indetermiiiates over A.Consider A[[Xa]]3 and its subrings A[[X_(A)]]_(1),A[[X_(A)]]_(2),and A[[X_(A)]]_(α),where a is an infinite cardinal number.In fact,a z-ideal of the rings defined above is of the form I+(X_(A))i,where i=1,2,3 or an infinite cardinal number and I is a z-ideal of A.In addition,we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients.As a natural result,we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.