The inverse hull of the free semigroup on a set X

1978 ◽  
Vol 16 (1) ◽  
pp. 345-354 ◽  
Author(s):  
Nathaniel Knox
Keyword(s):  

2011 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Alex Wright

AbstractWe show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.



1993 ◽  
Vol 03 (03) ◽  
pp. 335-347 ◽  
Author(s):  
V.S. GUBA
Keyword(s):  

Let m≥3, n≥1. In this article we show that the word problem for the relatively free Burnside semigroup satisfying Tm=Tm+n, is decidable.



1993 ◽  
Vol 36 (1) ◽  
pp. 49-54 ◽  
Author(s):  
John Baker ◽  
Neil Hindman ◽  
John Pym

Let S be a free semigroup (on any set of generators). When S is given the discrete topology, its Stone-Čech compactification has a natural semigroup structure. We give two results about elements p of finite order in βS. The first is that any continuous homomorphism of βS into any compact group must send p to the identity. The second shows that natural extensions, to elements of finite order, of relationships between idempotents and sequences with distinct finite sums, do not hold.







1980 ◽  
pp. 123-129 ◽  
Author(s):  
Renato M. Capocelli
Keyword(s):  


2020 ◽  
Vol 20 (05) ◽  
pp. 2050040
Author(s):  
Zhumin Ding ◽  
Jiandong Yin ◽  
Xiaofang Luo

In this paper, we introduce the conceptions of multi-transitivity, [Formula: see text]-transitivity and [Formula: see text]-mixing property for free semigroup actions and give some equivalent conditions for a free semigroup action to be multi-transitive, multi-transitive with respect to vectors and strongly multi-transitive, respectively. For instance, we prove that a free semigroup action is multi-transitive or multi-transitive with respect to a vector if and only if its corresponding skew product system is multi-transitive or multi-transitive with respect to the same vector.



1975 ◽  
Vol 20 (1) ◽  
pp. 110-114 ◽  
Author(s):  
G. R. Baird

A semigroup is said to be congruence-free if it has only two congruences, the identity congruence and the universal congruence. It is almost immediate that a congruence-free semigroup of order greater than two must either be simple or 0-simple. In this paper we describe the semilattices of congruence-free inverse semi-groups with zero. Further, congruence-free inverse semigroups with zero are characterized in terms of partial isomorphisms of their semilattices. A general discussion of congruence-free inverse semigroups, with and without zero, is given by Munn (to appear).





2009 ◽  
Vol 87 (2) ◽  
pp. 227-252 ◽  
Author(s):  
JOHN FOUNTAIN ◽  
MARK KAMBITES

AbstractOur first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialize to the case of the inverse hulls of graph monoids, obtaining what we call ‘polygraph monoids’. Among other properties, we observe that polygraph monoids are F*-inverse. This follows from a general characterization of those right cancellative monoids with inverse hulls that are F*-inverse.



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