scholarly journals On pseudo-distributive near-rings

1985 ◽  
Vol 28 (2) ◽  
pp. 133-141 ◽  
Author(s):  
Gordon Mason
Keyword(s):  
Group Ring ◽  
Finite Support ◽  
First Case ◽  
Image Position

If G is a group and N a ring, the elements of the group ring NG can be thought of either as formal sums or as functions Φ:G→Nwith finite support. If N is a nearring, problems arise in trying to construct a group near-ring either way. In the first case, Meldrum [7] was abl to exploit properties of distributively generated near-rings (N, S) to build free (N,S)-products and hence a near-ring analogue of a group ring. For the latter case, Heatherly and Ligh [3] observed that the set of functions could be made into a near-ring under multiplication given by provided N satisfiesfor all ai,bin∈N and k∈Z+. Such near-rings are called pseudo-distributive. In fact these are precisely the conditions under which the set Nk of k x k matrices over N is also a near-ring and then both NG and Nk are pseudo-distributive.

Central Idempotents in Group Rings

1970 ◽  
Vol 13 (4) ◽  
pp. 527-528 ◽  
Author(s):  
R. G. Burns
Keyword(s):  
Support Group ◽  
Group Ring ◽  
Group Rings ◽  
Finite Support ◽  
Image Position

Let R be a ring and G a group. The group ring RG consists of all functions f: G → R with finite support. Addition is pointwise and multiplication is defined for f, h ∊ RG and g ∊ G, byThe support group of f is defined to be the subgroup of G generated by the support of f. The element f is idempotent if ff = fWe prove the following result.

Shelah's work on non-semi-proper iterations, II

2001 ◽  
Vol 66 (4) ◽  
pp. 1865-1883 ◽  
Author(s):  
Chaz Schlindwein
Keyword(s):  
Closed Subset ◽  
Stationary Subset ◽  
Finite Support ◽  
Countable Support ◽  
Final Model ◽  
Axiom A ◽  
Mahlo Cardinal ◽  
The One ◽  
Image Position ◽  
Special Case

One of the main goals in the theory of forcing iteration is to formulate preservation theorems for not collapsing ω1 which are as general as possible. This line leads from c.c.c. forcings using finite support iterations to Axiom A forcings and proper forcings using countable support iterations to semi-proper forcings using revised countable support iterations, and more recently, in work of Shelah, to yet more general classes of posets. In this paper we concentrate on a special case of the very general iteration theorem of Shelah from [5, chapter XV]. The class of posets handled by this theorem includes all semi-proper posets and also includes, among others, Namba forcing.In [5, chapter XV] Shelah shows that, roughly, revised countable support forcing iterations in which the constituent posets are either semi-proper or Namba forcing or P[W] (the forcing for collapsing a stationary co-stationary subset ofwith countable conditions) do not collapse ℵ1. The iteration must contain sufficiently many cardinal collapses, for example, Levy collapses. The most easily quotable combinatorial application is the consistency (relative to a Mahlo cardinal) of ZFC + CH fails + whenever A ∪ B = ω2 then one of A or B contains an uncountable sequentially closed subset. The iteration Shelah uses to construct this model is built using P[W] to “attack” potential counterexamples, Levy collapses to ensure that the cardinals collapsed by the various P[W]'s are sufficiently well separated, and Cohen forcings to ensure the failure of CH in the final model.In this paper we give details of the iteration theorem, but we do not address the combinatorial applications such as the one quoted above.These theorems from [5, chapter XV] are closely related to earlier work of Shelah [5, chapter XI], which dealt with iterated Namba and P[W] without allowing arbitrary semi-proper forcings to be included in the iteration. By allowing the inclusion of semi-proper forcings, [5, chapter XV] generalizes the conjunction of [5, Theorem XI.3.6] with [5, Conclusion XI.6.7].

The Group Ring Of a Class Of Infinite Nilpotent Groups

1955 ◽  
Vol 7 ◽  
pp. 169-187 ◽  
Author(s):  
S. A. Jennings
Keyword(s):  
Nilpotent Group ◽  
Group Ring ◽  
Characteristic Zero ◽  
Discrete Group ◽  
Nilpotent Groups ◽  
Zero Element ◽  
Free Nilpotent Group ◽  
Image Position ◽  
Torsion Free ◽  
The Ideal

Introduction. In this paper we study the (discrete) group ring Γ of a finitely generated torsion free nilpotent group over a field of characteristic zero. We show that if Δ is the ideal of Γ spanned by all elements of the form G − 1, where G ∈ , thenand the only element belonging to Δw for all w is the zero element (cf. (4.3) below).

Comment on the paper ‘On the influence of the Hall effect on the spectrum of the ideal magnetohydrodynamic cylindrical pinch’ by U. Schaper

1984 ◽  
Vol 31 (1) ◽  
pp. 173-175 ◽  
Author(s):  
A. Lifshitz ◽  
E. Fedorov ◽  
U. Schaper
Keyword(s):  
Eigenvalue Problem ◽  
Hall Effect ◽  
Distributional Sense ◽  
General Properties ◽  
First Case ◽  
Ideal Magnetohydrodynamic ◽  
Image Position ◽  
The Continuum ◽  
The Ideal

General properties of the eigenvalues of Schaper (1983), concerning the continuum of eigenvalues on p. 7, needs correction. The solutions in the distributional sense of the eigenvalue problem (5.3), will be given for two cases. The first case has been solved by A. Lifshitz and E. Fedorov and concerns continuous eigenvalues. In the second case, the solution for the points of accumulation of discrete eigenvalues is discussed.

Natural maps of extension functors and a theorem of R. G. Swan

1961 ◽  
Vol 57 (3) ◽  
pp. 489-502 ◽  
Author(s):  
P. J. Hilton ◽  
D. Rees
Keyword(s):  
Finite Group ◽  
Exact Sequence ◽  
Group Ring ◽  
Projective Module ◽  
Additive Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Natural Maps ◽  
Image Position ◽  
A Finite Group

The present paper has been inspired by a theorem of Swan(5). The theorem can be described as follows. Let G be a finite group and let Γ be its integral group ring. We shall denote by Z an infinite cyclic additive group considered as a left Γ-module by defining gm = m for all g in G and m in Z. By a Tate resolution of Z is meant an exact sequencewhere Xn is a projective module for − ∞ < n < + ∞, and.

On Group Rings

1970 ◽  
Vol 22 (2) ◽  
pp. 249-254 ◽  
Author(s):  
D. B. Coleman
Keyword(s):  
Nilpotent Group ◽  
Commutative Ring ◽  
Group Ring ◽  
Characteristic Zero ◽  
Sylow Subgroup ◽  
Jacobson Radical ◽  
Closed Field ◽  
Group Rings ◽  
Locally Finite ◽  
Image Position

Let R be a commutative ring with unity and let G be a group. The group ring RG is a free R-module having the elements of G as a basis, with multiplication induced byThe first theorem in this paper deals with idempotents in RG and improves a result of Connell. In the second section we consider the Jacobson radical of RG, and we prove a theorem about a class of algebras that includes RG when G is locally finite and R is an algebraically closed field of characteristic zero. The last theorem shows that if R is a field and G is a finite nilpotent group, then RG determines RP for every Sylow subgroup P of G, regardless of the characteristic of R.

Significance of the Coupling between Saturation Vapour Pressure Deficit and Rainfall in Monsoon Climates

1986 ◽  
Vol 22 (4) ◽  
pp. 329-338 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Vapour Pressure ◽  
Dry Matter ◽  
Vapour Pressure Deficit ◽  
Supplemental Irrigation ◽  
First Case ◽  
Matter Production ◽  
Screen Height ◽  
Saturation Vapour Pressure ◽  
The Mean ◽  
Image Position

SUMMARYIn monsoon climates, the mean daytime saturation vapour pressure deficit (D), measured at screen height, decreases from a maximum of 3–4 kPa attained several months before rain arrives to a minimum of 0.5–1 kPa in the month of highest rainfall. Climatic records from India and West Africa were analysed to give the relation between D and precipitation (P mm month−1) as:where n ranged from 0.5 to 0.9 between stations.The dependence of dry matter production on D and therefore on P is evaluated when growth is restricted by rain and when this restriction is removed by irrigation. In the first case, the decrease in demand for water associated with a decrease in D is comparable in importance with the increase of water supply (P). The analysis has implications for the marginal response of crops to supplemental irrigation and for the interpretation of experiments with a line-source or rain-shelter.

scholarly journals COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS

2018 ◽  
Vol 83 (1) ◽  
pp. 208-236 ◽  
Author(s):  
VERA FISCHER ◽  
SY D. FRIEDMAN ◽  
DIEGO A. MEJÍA ◽  
DIANA C. MONTOYA
Keyword(s):  
Three Dimensional ◽  
Finite Support ◽  
Coherent Systems ◽  
Cichoń’S Diagram ◽  
Image Position ◽  
Generic Extensions

AbstractWe introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cichoń’s diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 values is consistent with the existence of a ${\rm{\Delta }}_3^1$ well-order of the reals.

scholarly journals C*-Algebras of inverse semigroups

1985 ◽  
Vol 28 (1) ◽  
pp. 41-58 ◽  
Author(s):  
J. Duncan ◽  
A. L. T. Paterson
Keyword(s):  
Banach Algebra ◽  
Group Ring ◽  
Discrete Group ◽  
Regular Representation ◽  
Inverse Semigroups ◽  
C Algebras ◽  
Complex Group ◽  
Left Regular Representation ◽  
Left Regular ◽  
Image Position

There are various algebras which may be associated with a discrete group G. In particular we may consider the complex group ring ℂG, the convolution Banach algebra l1(G), the enveloping C*-algebra C*(G) of l1(G), and the reduced C*-algebra determined by the completion of l1(G) under the left regular representation on l2(G). There is a substantial literature on the circle of ideas associated with the embeddings

The associated graded ring of an integral group ring

1977 ◽  
Vol 82 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Inder Bir S. Passi ◽  
Lekh Raj Vermani
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Symmetric Algebra ◽  
Integral Group Ring ◽  
Augmentation Ideal ◽  
Integral Group ◽  
Finite Abelian Groups ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Image Position

Let G be an Abelian group, the symmetric algebra of G and the associated graded ring of the integral group ring ZG, where (AG denotes the augmentation ideal of ZG). Then there is a natural epimorphism (4)which is given on the nth component byIn general θ is not an isomorphism. In fact Bachmann and Grünenfelder(1) have shown that for finite Abelian G, θ is an isomorphism if and only if G is cyclic. Thus it is of interest to investigate ker θn for finite Abelian groups. In view of proposition 3.25 of (3) it is enough to consider finite Abelian p-groups.

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