The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

Let R be a ring with Jacobson radical J and with center C. Let P be the set of potent elements x for which xk = x for some integer k > 1. Let N be the set of nilpotents. A ring R is called subperiodic if R \ (J ∪ C) ⊆ N + P . We consider the commutativity behavior of a subperiodic ring with some constraint involving extended commutators. Mathematics Subject Classification: 16U80, 16D70

We report the discovery, using NICMOS on the Hubble Space Telescope, of an arcsecond-diameter Einstein ring in the gravitational lens system B1938+666. The lensing galaxy is also detected, and is most likely an early-type. Modelling of the ring is presented and compared with the radio structure from MERLIN maps. We show that the Einstein ring is consistent with the gravitational lensing of an e...

In the title salt, C(21)H(18)ClNO, the quinoline ring system is approximately planar [maximum deviation = 0.035 (2) Å], and forms a dihedral angle of 71.42 (6)° with the attached phenyl ring. The cyclo-hexa-none ring exists in a half-boat conformation. In the crystal packing, C-H⋯O contacts link the mol-ecules into extended supra-molecular chains along the c axis.

As part of ASHRAE Research Project 1185, field data from the constant flow rate charging of a stratified chilled water storage tank with double-ring octagonal slotted-pipe diffusers serving a university chilled water system were compared with results of a transient axisymmetric computational fluid dynamics (CFD) model. Charge processes at flows near design flow rate and 50% of design were model...

The force measuring device is designed to the study of the relationship between vibration amplitude, frequency, speed and traction resistance of the tractor If the design of the force measuring device which consists of a force measuring frame and three octagonal ring transducers is successful, the goal of real-time monitoring of the traction resistance in the process of vibrating sub soil may b...