scholarly journals A combinatorial approach to the structure of locally inverse semigroups

2021 ◽  
Author(s):  
Luís Oliveira
Keyword(s):  
Inverse Semigroups ◽  
Combinatorial Approach ◽  
Locally 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.

Maximal Dense Ideal Extensions of Locally Inverse Semigroups

2006 ◽  
Vol 72 (3) ◽  
pp. 441-458 ◽  
Author(s):  
F.J. Pastijn ◽  
L. Oliveira
Keyword(s):  
Inverse Semigroups ◽  
Dense Ideal ◽  
Locally Inverse Semigroups

ALMOST FACTORIZABLE LOCALLY INVERSE SEMIGROUPS

2011 ◽  
Vol 21 (07) ◽  
pp. 1037-1052 ◽  
Author(s):  
MÁRIA B. SZENDREI
Keyword(s):  
Inverse Semigroups ◽  
Completely Simple Semigroups ◽  
Order Ideals ◽  
Locally Inverse Semigroups ◽  
Completely Simple

We introduce a notion of almost factorizability within the class of all locally inverse semigroups by requiring a property of order ideals, and we prove that the almost factorizable locally inverse semigroups are just the homomorphic images of Pastijn products of normal bands by completely simple semigroups.

scholarly journals Identities for existence varieties of regular semigroups

1989 ◽  
Vol 40 (1) ◽  
pp. 59-77 ◽  
Author(s):  
T.E. Hall
Keyword(s):  
Type Theorem ◽  
Inverse Semigroups ◽  
Direct Products ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Existence Variety ◽  
Completely Regular Semigroups ◽  
Locally Inverse Semigroups ◽  
Orthodox Semigroups ◽  
Regular Rings

A natural concept of variety for regular semigroups is introduced: an existence variety (or e-variety) of regular semigroups is a class of regular semigroups closed under the operations H, Se, P of taking all homomorphic images, regular subsernigroups and direct products respectively. Examples include the class of orthodox semigroups, the class of (regular) locally inverse semigroups and the class of regular E-solid semigroups. The lattice of e-varieties of regular semigroups includes the lattices of varieties of inverse semigroups and of completely regular semigroups. A Birkhoff-type theorem is proved, showing that each e-variety is determined by a set of identities: such identities are then given for many e-varieties. The concept is meaningful in universal algebra, and as for regular semigroups could give interesting results for e-varieties of regular rings.

scholarly journals On the variety of strict pseudosemilattices

2013 ◽  
Vol 50 (2) ◽  
pp. 207-241 ◽  
Author(s):  
K. Auinger ◽  
L. Oliveira
Keyword(s):  
Bipartite Graphs ◽  
Inverse Semigroups ◽  
Finitely Based ◽  
New Model ◽  
Locally Inverse Semigroups

A new model, in terms of finite bipartite graphs, of the free pseudosemilattice is presented. This will then be used to obtain several results about the variety SPS of all strict pseudosemilattices: (i) an identity basis for SPS is found, (ii) SPS is shown to be inherently non-finitely based, (iii) SPS is shown to have no irredundant identity basis, and (iv) SPS is shown to have no covers and to be ∩-prime in the lattice of all varieties of pseudosemilattices. Some applications to e-varieties of locally inverse semigroups are also derived.

On the Lattice of Existence Varieties of Locally Inverse Semigroups

1994 ◽  
Vol 37 (1) ◽  
pp. 13-20 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroups ◽  
Surjective Homomorphism ◽  
Lattice Of Varieties ◽  
Existence Variety ◽  
Locally Inverse Semigroups

AbstractThe mapping which assigns to each existence variety of locally inverse semigroups the class of all pseudosemilattices of idempotents of members of is shown to be a complete, surjective homomorphism from the lattice of existence varieties of locally inverse semigroups onto the lattice of varieties of pseudosemilattices.

Ideal extensions of locally inverse semigroups

2008 ◽  
Vol 45 (3) ◽  
pp. 395-409 ◽  
Author(s):  
Francis Pastijn ◽  
Luís Oliveira
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Inverse Subsemigroup ◽  
Locally Inverse Semigroup ◽  
Locally Inverse Semigroups

The translational hull of a locally inverse semigroup has a largest locally inverse subsemigroup containing the inner part. A construction is given for ideal extensions within the class of all locally inverse semigroups.

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