On the Circle Group of a Nilpotent Ring

1970 ◽  
Vol 77 (2) ◽  
pp. 168 ◽  
Author(s):  
R. L. Kruse
Keyword(s):  
Circle Group ◽  
Nilpotent Ring

Circle Group Packing Algorithm for Mosaic Synthesis

2018 ◽  
Vol 30 (7) ◽  
pp. 1216
Author(s):  
Kai Zhang ◽  
Ying Ke ◽  
Juan Cao ◽  
Zhonggui Chen
Keyword(s):  
Circle Group ◽  
Packing Algorithm

scholarly journals Notes on topological rings

2013 ◽  
Vol 29 (2) ◽  
pp. 267-273
Author(s):  
MIHAIL URSUL ◽  
◽  
MARTIN JURAS ◽  
Keyword(s):  
Principal Ideal ◽  
Principal Ideal Domain ◽  
Compact Ring ◽  
Ring Topology ◽  
Bezout Domain ◽  
Totally Bounded ◽  
Ideal Domain ◽  
Nilpotent Ring ◽  
Trivial Multiplication

We prove that every infinite nilpotent ring R admits a ring topology T for which (R, T ) has an open totally bounded countable subring with trivial multiplication. A new example of a compact ring R for which R2 is not closed, is given. We prove that every compact Bezout domain is a principal ideal domain.

Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on 𝕋

2009 ◽  
Vol 30 (1) ◽  
pp. 151-157 ◽  
Author(s):  
MANFRED EINSIEDLER ◽  
ALEXANDER FISH
Keyword(s):  
Probability Measure ◽  
Polynomial Growth ◽  
Borel Probability Measure ◽  
Finite Support ◽  
Multiplicative Semigroup ◽  
Logarithmic Density ◽  
Circle Group ◽  
Borel Probability

AbstractWe prove that if a Borel probability measure on the circle group is invariant under the action of a ‘large’ multiplicative semigroup (lower logarithmic density is positive) and the action of the whole semigroup is ergodic then the measure is either Lebesgue or has finite support.

Some Simple Properties of Simple Nil Rings

1966 ◽  
Vol 9 (2) ◽  
pp. 197-200 ◽  
Author(s):  
W. A. McWorter
Keyword(s):  
Unsolved Problem ◽  
Finitely Generated ◽  
Nilpotent Ring ◽  
Locally Nilpotent ◽  
Nil Ring

An outstanding unsolved problem in the theory of rings is the existence or non-existence of a simple nil ring. Such a ring cannot be locally nilpotent as is well known [ 5 ]. Hence, if a simple nil ring were to exist, it would follow that there exists a finitely generated nil ring which is not nilpotent. This seemed an unlikely situation until the appearance of Golod's paper [ 1 ] where a finitely generated, non-nilpotent ring is constructed for any d ≥ 2 generators over any field.

scholarly journals Remarks on multipliers on certain function spaces on groups

1981 ◽  
Vol 31 (3) ◽  
pp. 276-288
Author(s):  
Hiroshi Yamaguchi
Keyword(s):  
Hardy Spaces ◽  
Function Spaces ◽  
Circle Group ◽  
Positive Elements ◽  
Lca Group

AbstractLet G be LCA group with an algebraically ordered dual Ĝ. Suppose also that the semigroup P of positive elements in Ĝ is not dense in Ĝ. Subspaces (G) (1 < s < ∞) are defined analogous to the Hardy spaces on the circle group, and the question whether every multiplier from into can be extended to a multiplier from L3(G) into Lq(G) is investigated. If we suppose that s ≠ ∞, the it is shown that such an extension is possible if and only if (s, q) ∈ (1, ∞) × [1, ∞] ∪ {(1, ∞)}. (the negative result for (1, 1) was obtained in a previous paper.)

scholarly journals The class L(log L)α and some lacunary sets

1995 ◽  
Vol 58 (3) ◽  
pp. 387-403
Author(s):  
Sanjiv Kumar Gupta ◽  
Shobha Madan ◽  
U. B. Tewari
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Circle Group ◽  
New Class ◽  
Special Cases ◽  
L Log L

AbstractA well-known result of Zygmund states that if f ∈ L (log+L) ½ on the circle group T and E is a Hadamard set of integers, then . In this paper we investigate similar results for the classes on an arbitrary infinite compact abelian group G and Sidon subsets E of the dual Γ. These results are obtained as special cases of more general results concerning a new class of lacunary sets Sαβ, 0 < α ≤ β, where a subset E of Γ is an Sα β set if . We also prove partial results on the distinctness of the Sαβ sets in the index β.

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