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81.
V. Yu. Popov 《Mathematical Notes》2000,67(4):495-504
An example of a series of varieties of rings
with the finite basis property is constructed for which the word problem in the relatively free ring
of rankn in the variety
is decidable if and only ifn <p.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000. 相似文献
82.
K. Varadarajan 《Proceedings Mathematical Sciences》2000,110(2):133-136
Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring
to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF. 相似文献
83.
Yiqiang Zhou 《Algebra Colloquium》2000,7(3):305-318
For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(RR) = Jac(R/Soc(RR)) and show, among others, the following results:
The research was partially supported by the NSERC of Canada under Grant OGP0194196.2000 Mathematics Subject Classification: 16L30, 16E50 相似文献
(1) | (R) is the largest -small right ideal of R. |
(2) | R is -semiregular if and only if R/(R) is a von Neumann regular ring and idempotents of R(R) lift to idempotents of R. |
(3) | R is -semiperfect if and only if R/(R) is a semisimple ring and idempotents of R/(R) lift to idempotents of R. |
(4) | R is -perfect if and only if R/Soc(RR) is a right perfect ring and idempotents of R/(R) lift to idempotents of R. |
84.
Hans H. Brungs Joachim Grä ter 《Transactions of the American Mathematical Society》2000,352(7):3357-3379
A subring of a division algebra is called a valuation ring of if or holds for all nonzero in . The set of all valuation rings of is a partially ordered set with respect to inclusion, having as its maximal element. As a graph is a rooted tree (called the valuation tree of ), and in contrast to the commutative case, may have finitely many but more than one vertices. This paper is mainly concerned with the question of whether each finite, rooted tree can be realized as a valuation tree of a division algebra , and one main result here is a positive answer to this question where can be chosen as a quaternion division algebra over a commutative field.
85.
Alessandro Berarducci 《Transactions of the American Mathematical Society》2000,352(2):553-577
The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.
86.
Ring structures in telecommunications are taking on increasing importance because of their self-healing properties. We consider a ring design problem in which several stacked self-healing rings (SHRs) follow the same route, and, thus, pass through the same set of nodes. Traffic can be exchanged among these stacked rings at a designated hub node. Each non-hub node may be connected to multiple rings. It is necessary to determine to which rings each node should be connected, and how traffic should be routed on the rings. The objective is to optimize the tradeoff between the costs for connecting nodes to rings and the costs for routing demand on multiple rings. We describe a genetic algorithm that finds heuristic solutions for this problem. The initial generation of solutions includes randomly-generated solutions, complemented by seed solutions obtained by applying a greedy randomized adaptive search procedure (GRASP) to two related problems. Subsequent generations are created by recombining pairs of parent solutions. Computational experiments compare the genetic algorithm with a commercial integer programming package. 相似文献
87.
I.B. Khriplovich 《Hyperfine Interactions》2000,127(1-4):365-371
Upper limits on the electric dipole moments (EDM) of elementary particles and atoms are presented, and their physical implications
are discussed. The implications following from the neutron and atomic experiments are of comparable interest. The nuclear
EDMs can be studied at ion storage rings, with the expected sensitivity much better than
. This would represent a serious progress in studies of the CP-violation problem.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
88.
A nonlinear (piecewise linear) optical transfer function for optical applications generally and isolator especially is introduced and a realization method for the introduced block based on array of two-port nonlinear ring resonators is proposed. The effect of system parameters on the transfer function is studied. The characteristics of the introduced nonlinear device such as the threshold value and the slope of linear part can be controlled using the coupling coefficients and ring lengths. We show that using our proposed idea, easily more than 30-dB isolation well over 3 THz can be obtained only with similar two rings. Also, insertion loss less than 1 dB can be obtained using optical amplifier between rings. The proposed circuit is compact (0.2 mm2) and easily can be integrated with semiconductor lasers as well as other integrated devices and systems. Finally, the analytical result for approximation of the threshold and slope of linear part is presented. 相似文献
89.
《代数通讯》2013,41(9):4291-4299
Abstract Marciniak and Sehgal (Marciniak, Z., Sehgal, S. K. (1997). Constructing free subgroups of integral group rings units. Proc. Amer. Math. Soc.125(4):1005–1009) constructed free subgroups in U(?[G]) whenever Ghas a non normal finite subgroup. In this paper we construct free subgroups in U(?[G]), where Gis a group whose subgroups are all normal. 相似文献
90.
Gorenstein flatness and injectivity over Gorenstein rings 总被引:1,自引:0,他引:1
Let R be a Gorenstein ring.We prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical.In addition,we prove that if R→S is a homomorphism of rings and SE is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical.We also give some applications of these results. 相似文献