Rectangular group compactification of a semigroup

2007 ◽  
Vol 2 ◽  
pp. 1263-1269
Author(s):  
A. Jabbari ◽  
H. R. E. Vishki
Keyword(s):  
Rectangular Group

scholarly journals Rectangular group congruences on a semigroup

2012 ◽  
Vol 87 (1) ◽  
pp. 120-128 ◽  
Author(s):  
Roman S. Gigoń
Keyword(s):  
Rectangular Group

Independent domination number in Cayley digraphs of rectangular groups

2018 ◽  
Vol 10 (02) ◽  
pp. 1850024
Author(s):  
Nuttawoot Nupo ◽  
Sayan Panma
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Independent Set ◽  
Left Zero ◽  
Zero Semigroup ◽  
Left Zero Semigroup ◽  
Group A ◽  
Independent Domination ◽  
Independent Dominating Set ◽  
Rectangular Group

Let [Formula: see text] denote the Cayley digraph of the rectangular group [Formula: see text] with respect to the connection set [Formula: see text] in which the rectangular group [Formula: see text] is isomorphic to the direct product of a group, a left zero semigroup, and a right zero semigroup. An independent dominating set of [Formula: see text] is the independent set of elements in [Formula: see text] that can dominate the whole elements. In this paper, we investigate the independent domination number of [Formula: see text] and give more results on Cayley digraphs of left groups and right groups which are specific cases of rectangular groups. Moreover, some results of the path independent domination number of [Formula: see text] are also shown.

scholarly journals FREE PROFINITE SEMIGROUPS OVER SOME CLASSES OF SEMIGROUPS LOCALLY IN ${\mathcal D} {\rm G}$

2000 ◽  
Vol 10 (04) ◽  
pp. 491-537 ◽  
Author(s):  
JOSÉ CARLOS COSTA
Keyword(s):  
Rectangular Group

This paper is concerned with the structure of semigroups of implicit operations on various subpseudovarieties V of [Formula: see text] ∩ [Formula: see text], where [Formula: see text] and [Formula: see text] are the pseudovarieties of all semigroups S in which each regular [Formula: see text] -class is, respectively, a rectangular group and a group, and where [Formula: see text] is the pseudovariety of semigroups locally in [Formula: see text] As an application, we give a characterization of the variety of languages recognized by semigroups in V and derive some join decompositions of pseudovarieties.

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