power semigroup
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1996 ◽  
Vol 38 (1) ◽  
pp. 39-47
Author(s):  
David Easdown ◽  
Victoria Gould
Keyword(s):  

In this paper we consider examples of orders in restricted power semigroups, where for any semigroup Sthe restricted power semigroup is given by with multiplication XY = {xy:x ∈ X, y ∈ Y} for all X, Y ∈ . We use the notion of order introduced by Fountain and Petrich in [2] which first appears in the form used here in [3]. If S is a subsemigroup of Q then S is an order in Q and Q is a semigroup of quotients of S if any q ∈ Q can be written as q = a*b = cd* where a, b, c, d ∈ S is the inverse of a(d) in a subgroup of Q, and in addition, all elements of S satisfying a weak cancellability condition called square-cancellability lie in a subgroup of Q.





1984 ◽  
Vol 60 (10) ◽  
pp. 388-390 ◽  
Author(s):  
Takayuki Tamura
Keyword(s):  


1979 ◽  
Vol 31 (5) ◽  
pp. 1077-1083 ◽  
Author(s):  
Mohan S. Putcha

Throughout this paper, S will denote a finite semigroup and Z+ the set of positive integers. E = E(S) denotes the set of idempotents of S. Let . If , then let AB = {ab| a ∈ A, b ∈ B}. has been studied by many authors, including [2, 3, 5, 6, 7]. If X is a set, then |X| denotes the cardinality of X. For undefined terms in this paper, see [1,4].THEOREM 1. Let I be an ideal of S, a subgroup of . Then has a normal subgroups such that is isomorphic to a subgroup of and is isomorphic to a subgroup of .



1977 ◽  
Vol 15 (1) ◽  
pp. 263-267 ◽  
Author(s):  
Mohan S. Putcha


1973 ◽  
Vol 14 (2) ◽  
pp. 173-186 ◽  
Author(s):  
Donald J McCarthy ◽  
David L Hayes
Keyword(s):  


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