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1.
Lattice orders on the semigroup ring of a positive rooted monoid are constructed, and it is shown how to make the monoid ring into a lattice-ordered ring with squares positive in various ways. It is proved that under certain conditions these are all of the lattice orders that make the monoid ring into a lattice-ordered ring. In particular, all of the partial orders on the polynomial ring A[x] in one positive variable are determined for which the ring is not totally ordered but is a lattice-ordered ring with the property that the square of every element is positive. In the last section some basic properties of d-elements are considered, and they are used to characterize lattice-ordered division rings that are quadratic extensions of totally ordered division rings. 相似文献
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V.V. Bavula 《Journal of Pure and Applied Algebra》2018,222(7):1548-1564
Two criteria are given for a ring to have a left Noetherian left quotient ring (to find a criterion was an open problem since 70's). It is proved that each such ring has only finitely many maximal left denominator sets. 相似文献
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Ana S?l?gean 《Discrete Applied Mathematics》2006,154(2):413-419
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring. 相似文献
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The initial non-linearly elastic stage of a change in the shape of thin flexible ring under an external hydrostatic pressure is described. At this stage, the formation of alternating bulges and hollows in the ring in a circular direction is due to the balance of non-linearity and dispersion effects. A model is proposed which enables the dependence of the curvature of the deformed ring on the external pressure to be obtained. The shape of the ring is established from the known curvature by methods of differential geometry. Possible types of corrugation of the initial circular ring are obtained. The change in the shape of the ring around a rigid rod, placed inside the ring, is described. The strict relation between the amplitude of the bulges and hollows in the circumferential direction of the ring also prevents the formation of rigid edges on its surface. 相似文献
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Murray Marshall 《代数通讯》2013,41(3):1157-1173
The object of the paper is to extend part of the theory of *-orderings on a skewfield with involution to a general ring with involution. The valuation associated to a *-ordering is examined. Every *-ordering is shown to extend. *-orderings are shown to form a space of signs as defined by Brocker and Marshall. In case the involution is the identity, the ring under consideration is commutative and the *-orderings are just the usual orderings making up the usual real spectrum of a commutative ring as defined by Coste and Roy. 相似文献
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Exact analytical solutions of problems on the static and dynamic forms of the loss of stability of a ring, under the action of a linear torque constant along the perimeter, are found using the consistent equations of the theory of plane curvilinear rods constructed earlier taking account of transverse shears. Two forms of torsion of the ring are examined: the external forces creating a torque remain in the plane of a cross-section of the ring in its initial undeformed state (“dead” forces, case 1) or in its deformed state (“follower” forces, case 2). It is shown that, in the second case, the solution of the static instability problem found is practically identical to the solution of the problem corresponding to the dynamic formulation and is reduced to an examination of the oscillations about the static equilibrium position. In the case of both forms of loading, loss of stability of the ring occurs without deformation of its axial line, with it bending predominantly in the plane of the ring accompanied by a slight distortion. It is established that a study of the forms of loss of stability of the ring for the type of loading considered is only possible using the equations constructed, taking account of transverse shear. 相似文献
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For an endomorphism α of a ring R, we introduce the notion of an α-Armendariz ring to investigate the relative Armendariz properties. This concept extends the class of Armendariz rings and gives us an opportunity to study Armendariz rings in a general setting. It is obvious that every Armendariz ring is an α-Armendariz ring, but we shall give an example to show that there exists a right α-Armendariz ring which is not Armendariz. A number of properties of this version are established. It is shown that if I is a reduced ideal of a ring R such that R/I is a right α-Armendariz ring, then R is right α-Armendariz. For an endomorphism α of a ring R, we show that R is right α-Armendariz if and only if R[x] is right α-Armendariz. Moreover, a weak form of α-Armendariz rings is considered in the last section. We show that in general weak α-Armendariz rings need not be α-Armendariz. 相似文献
9.
Dejun Wu 《Czechoslovak Mathematical Journal》2014,64(2):567-579
We study the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex. Some results that track the behavior of Gorenstein properties over local ring homomorphisms under composition and decomposition are given. As an application, we characterize a dualizing complex for R in terms of the finiteness of the G-dimension over local ring homomorphisms with respect to a semi-dualizing complex. 相似文献
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本文给出了代数A与双代数H的Smash积AH是A的超限左自由正规化扩张的一个充分条件.进一步,主要结果被运用到斜半群环、斜群环和量子群Uq(sl(2))从而给出了它们的一些性质. 相似文献
12.
A two-layer ring, with account of its initial state caused by internal pressure and corrosion, leading to wear, is considered.
The ring is subjected to an additional pressure causing its radial vibrations. It is shown that, under certain conditions,
there is a vibration frequency at which the delamination of the ring is possible. Expressions are found which determine this
frequency as a function of problem parameters, in particular, of the time of corrosive wear. 相似文献
13.
M. A. Lukin 《Russian Mathematics (Iz VUZ)》2008,52(12):65-68
We describe the structure of semirings which are unions of a ring and a half-body. 相似文献
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Let Ks(R) be the generalized matrix ring over a ring R with multiplier s. For a general local ring R and a central element s in the Jacobson radical of R, necessary and sufficient conditions are obtained for Ks(R) to be a strongly clean ring. For a commutative local ring R and an arbitrary element s in R, criteria are obtained for a single element of Ks(R) to be strongly clean and, respectively, for the ring Ks(R) to be strongly clean. Specializing to s = 1 yields some known results. New families of strongly clean rings are presented. 相似文献
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Jinzhong Xu 《代数通讯》2013,41(2):535-537
In this short paper, the homological functors are used to show that a simple module is flat if and only if it is injective. It is used to give a characterization of Von Neumann regular ring, that is, a commutative ring is Von Neuman regular if and only if every simple module is injective. 相似文献