Congruences on generalized inverse semigroups

1972 ◽  
Vol 4 (1) ◽  
pp. 200-205 ◽  
Author(s):  
G. R. Baird
Keyword(s):  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Generalized Inverse Semigroups

REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS

1996 ◽  
Vol 06 (05) ◽  
pp. 541-551
Author(s):  
TERUO IMAOKA ◽  
ISAMU INATA ◽  
HIROAKI YOKOYAMA
Keyword(s):  
Inverse Semigroup ◽  
Wreath Product ◽  
Representation Theorem ◽  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Locally Inverse Semigroup ◽  
The One ◽  
Locally Inverse Semigroups ◽  
Generalized Inverse Semigroups

The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *-semigroup on a π-set, and show that any locally inverse *-semigroup can be embedded up to *-isomorphism in the π-symmetric locally inverse semigroup on a π-set. Moreover, we shall obtain that the wreath product of locally inverse *-semigroups is also a locally inverse *-semigroup.

scholarly journals Congruences and Green's relations on regular semigroups

1972 ◽  
Vol 13 (2) ◽  
pp. 167-175 ◽  
Author(s):  
T. E. Hall
Keyword(s):  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
Green's Relations ◽  
Generalized Inverse Semigroups

It is sometimes possible to reconstruct semigroups from some of their homomorphic images. Some recent examples have been the construction of bisimple inverse semigroups from fundamental bisimple inverse semigroups [9], and the construction of generalized inverse semigroups from inverse semigroups [12].

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