fundamental semigroups
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2010 ◽  
Vol 81 (1) ◽  
pp. 85-101 ◽  
Author(s):  
David Easdown ◽  
Patrick Jordan ◽  
Brad Roberts

2008 ◽  
Vol 77 (2) ◽  
pp. 279-299 ◽  
Author(s):  
Gracinda M. S. Gomes ◽  
Victoria Gould

2006 ◽  
Vol 14 (3) ◽  
pp. 447-463
Author(s):  
Fritz Colonius ◽  
◽  
Marco Spadini ◽  

2005 ◽  
Vol 185 (S5) ◽  
pp. S69-S91
Author(s):  
Fritz Colonius ◽  
Luiz A.B. San Martin ◽  
Marco Spadini

1988 ◽  
Vol 31 (3) ◽  
pp. 463-467 ◽  
Author(s):  
David Easdown

In any extension theory for semigroups one must determine the basic building blocks and then discover how they fit together to create more complicated semigroups. For example, in group theory the basic building blocks are simple groups. In semigroup theory however there are several natural choices. One that has received considerable attention, particularly since the seminal work on inverse semigroups by Munn ([14, 15]), is the notion of a fundamental semigroup. A semigroup is called fundamental if it cannot be [shrunk] homomorphically without collapsing some of its idempotents (see below for a precise definition).


Author(s):  
P. M. Edwards

SynopsisAn idempotent-separating congruence μ is studied further in this paper. It is shown to satisfy special properties with respect to regular elements and to group-bound elements. It is shown that for any semigroup S, μ is the identity congruence on S/μ. From this, it can be shown that S/μ is fundamental for any semigroup S. Some alternative characterizations of μ are given and applied to yield sufficient conditions for a subsemigroup T of S to satisfy μ (T) = μ (S) ∩ (T × T), whence T is fundamental if S is fundamental.


1980 ◽  
Vol 29 (4) ◽  
pp. 475-503 ◽  
Author(s):  
D. B. McAlister

AbstractIn this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.


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