On the lattice of completely regular monoid varieties

1993 ◽  
Vol 46 (1) ◽  
pp. 168-186
Author(s):  
Colleen Vachuska
Keyword(s):  
Completely Regular ◽  
Regular Monoid

scholarly journals Direct finiteness of certain monoid algebras

1996 ◽  
Vol 39 (2) ◽  
pp. 365-369 ◽  
Author(s):  
W. D. Munn
Keyword(s):  
Characteristic Zero ◽  
Completely Regular ◽  
Regular Monoid

A semigroup is said to be completely regular if and only if each of its elements lies in a subgroup. It is shown that the algebra of a completely regular monoid (semigroup with identity) over a field of characteristic zero is directly finite.

scholarly journals On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

scholarly journals Complete regularity of Ellis semigroups of -actions

2020 ◽  
pp. 1-17
Author(s):  
MARCY BARGE ◽  
JOHANNES KELLENDONK
Keyword(s):  
Complete Regularity ◽  
Completely Regular ◽  
Ellis Semigroup ◽  
Totally Disconnected

Abstract It is shown that the Ellis semigroup of a $\mathbb Z$ -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$ - or $\mathbb R$ -action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

scholarly journals Two semigroups of continuous relations

1977 ◽  
Vol 23 (1) ◽  
pp. 46-58 ◽  
Author(s):  
A. R. Bednarek ◽  
Eugene M. Norris
Keyword(s):  
Large Class ◽  
Algebraic Structure ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Completely Regular ◽  
Topological Semigroups ◽  
Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

Globals of completely regular periodic semigroups

1984 ◽  
Vol 29 (1) ◽  
pp. 365-374 ◽  
Author(s):  
Matthew Gould ◽  
Joseph A. Iskra ◽  
Constantine Tsinakis
Keyword(s):  
Completely Regular

Congruences on ideal nil-extension of completely regular semigroups

1998 ◽  
Vol 43 (5) ◽  
pp. 379-381
Author(s):  
Xueming Ren ◽  
Yuqi Guo ◽  
Jiaping Cen
Keyword(s):  
Regular Semigroups ◽  
Completely Regular ◽  
Completely Regular Semigroups ◽  
Nil Extension

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

A Regular Space, Not Completely Regular

1969 ◽  
Vol 76 (2) ◽  
pp. 181 ◽  
Author(s):  
John Thomas
Keyword(s):  
Regular Space ◽  
Completely Regular
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