Search

A ring R is called a generalized quasinormal ring (abbreviated as GQN ring) if ea ∈ N(R) for each e ∈ E(R) and a ∈ N(R) . The class of GQN rings is a proper generalization of quasinormal rings and NI rings. Many properties of quasinormal rings are extended to GQN rings. For a GQN ring R and a ∈ R, it is shown that: 1) if a is a regular element, then a is a strongly regular element; 2) if a is an exchange element, then a is clean; 3) if R is a semiperiodic ring with J(R) ≠ N(R) , then R is commutative; 4) if R is an MV NR, then R is strongly regular. [ABSTRACT FROM AUTHOR]

In this note, we first show that a ring R is Abel if and only if the 2 × 2 upper triangular matrix ring (R R/o R) over R is quasi-normal. Next, we give the notion of super-strongly clean ring (that is, an Abel clean ring), which is inbetween uniquely clean rings and strongly clean rings. Some characterizations of super-strongly clean rings are given. [ABSTRACT FROM AUTHOR]

Polymer membranes have been widely used in guided tissue regeneration (GTR) and guided bone regeneration (GBR). In this review, various commercially available membranes are described. Much attention is paid to the recent development of biodegradable polymers applied in GTR and GBR, and the important issues of biodegradable polymeric membranes, including their classification, latest experimental research and clinical applications, as well as their main challenges are addressed. Herein, natural polymers, synthetic polymers and their blends are all introduced. Pure polymer membranes are biodegradable and biocompatible, but they lack special properties such as antibacterial properties, osteoconductivity, and thus polymer membranes loaded with functional materials such as antibacterial agents and growth factors show many more advantages and have also been introduced in this review. Despite there still being complaints about polymer membranes, such as their low mechanical properties, uncontrollable degradation speed and some other drawbacks, these problems will undoubtedly be conquered and biodegradable polymers will have more applications in GTR and GBR. [ABSTRACT FROM AUTHOR]

A ring $$R$$ is $$CN$$ if and only if for any $$x\in N(R)$$ and $$y\in R$$ , $$((1+x)y)^{n+k}=(1+x)^{n+k}y^{n+k}$$ , where $$n$$ is a fixed positive integer and $$k=0, 1,2$$ ; (2) Let $$R$$ be a $$CN$$ ring and $$n\ge 1$$ . If for any $$x, y\in R\backslash N(R)$$ , $$(xy)^{n+k}=x^{n+k}y^{n+k}$$ , where $$k=0, 1,2$$ , then $$R$$ is commutative; (3) Let $$R$$ be a ring and $$n\ge 1$$ . If for any $$x\in R\backslash N(R)$$ and $$y\in R$$ , $$(xy)^k=x^ky^k$$ , $$k=n, n+1, n+2$$ , then $$R$$ is commutative; (4) $$NLI $$ exchange rings are clean. [ABSTRACT FROM AUTHOR]

A ring R is called NZI if for any a ∈ R, l(a) is an N-ideal of R. In this paper, we first study some basic properties and basic extensions of NZI rings. Next, we study the strong regularity of NZI rings and obtain the following results: (1) Let R be a left SF-ring. Then R is a strongly regular ring if and only if R is an NZI ring; (2) If R is an NZI left MC2 ring and every simple singular left R [ABSTRACT FROM AUTHOR]

To account for the phenomenon that the winding inter-turn short circuit fault of the turbine generator rotor leads to intensified vibration, a coupled nonlinear vibration model of the oil film force and electromagnetic force is established, and a dynamic stability analysis method is proposed. An improved shooting method for solving the periodic solutions of the bearing- rotor system with the unbalanced electromagnetic force is developed; and the system damping criterion used in examining the system stability margin is presented. The calculation on the nonlinear vibration for the 300 MW turbine generator is finished, and the vibration response characteristics and instability margin in a typical winding inter-turn short circuit fault are obtained. The results show that the winding inter-turn short circuit fault may result in the synchronized vortex phenomenon, and a comparison between the numerical results and the site test results is completed. The results will provide technical support and theoretical basis for directly predicting the winding inter-turn short-circuit fault via the vibration detection. [ABSTRACT FROM AUTHOR]

We investigate in this paper rings containing a non-essential nil -- injective maximal left ideal. We show that if R is a left MC2 ring containing a non-essential nil -- injective maximal left ideal, then R is a left nil -- injective ring. Using this result, some known results are extended. [ABSTRACT FROM AUTHOR]

A ring R is defined to be weakly normal if for all a, r ∈ R and e ∈ E(R), ae = 0 implies Rera is a nil left ideal of R, where E(R) stands for the set of all idempotent elements of R. It is proved that R is weakly normal if and only if Rer(1 -- e) is a nil left ideal of R for each e ∈ E(R) and r ∈ R if and only if Tn(R, R) is weakly normal for any positive integer n. And it follows that for a weakly normal ring R (1) R is Abelian if and only if R is strongly left idempotent reflexive; (2) R is reduced if and only if R is n-regular; (3) R is strongly regular if and only if R is regular; (4) R is clean if and only if R is exchange. (5) exchange rings have stable range 1. [ABSTRACT FROM AUTHOR]

In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1 - e)Re = 0 for alle ∈ MEl(R) ; (2) Quasi-normal rings, NI rings and weakly reversible rings are all minleftsemicentral ring; (3) R is left MC2 ring if and only if aRe = 0 implies eRa = 0 for alle ∈ MEl(R) and a ∈ R if and only if every projective simple left R-module is MUP -injective; (4) R is reduced if and only if R is n-regular and quasi-normal if and only if R is n-regular and weakly reversible; (5) R is strongly regular if and only if R is regular and quasi-normal if and only if R is regular and weakly reversible. [ABSTRACT FROM AUTHOR]

We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on strongly regular rings. [ABSTRACT FROM AUTHOR]

We introduce in this paper the concepts of rings characterized by minimal one-sided ideals and concern ourselves with rings containing an injective maximal left ideal. Some known results for idempotent reflexive rings and left HI rings can be extended to left MC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with non-zero socle and extend some known results for strongly regular rings. [ABSTRACT FROM AUTHOR]

In this paper, we first study some characterizations of left min-abel ring, strongly left min-abel ring and left MC2 ring. Next, we discuss and generalize some well known results for a ring whose simple singular left modules are nil - injective. Finally, as a byproduct of these results we are able to show that if R is a left GMC2 left Goldie ring whose every simple singular left R- module is Y J- injective, then R is a finite product of simple left Goldie ring. [ABSTRACT FROM AUTHOR]

A ring R is called JTTC if for any a∈N(R) and b∈R, (ab)²=ab²a, which is a proper generalization of CN rings. In this paper, we show that (1) a ring R is commutative if and only if (xy)²=xy²x for each x∈SN(R) and y∈SZr(R); (2) R is a JTTC ring if and only if xyx=x²y for each x∈N(R) and y∈SZr(R); (3) R is a reduced ring if and only if T³(R) is a JTTC ring; (4) R is a CN ring if and only if V²(R) is a JTTC ring; (5) R is a commutative reduced ring if and only if TV4(R) is a JTTC ring; (6) R is a commutative ring if and only if G³(R) is a JTTC ring; (7) If R is a JTTC ring containing a von Neumann regular maximal left ideal, then R is a strongly regular ring. [ABSTRACT FROM AUTHOR]