THE ORBIT STRUCTURE OF FINITE MONOIDS
1993 ◽
Vol 03
(04)
◽
pp. 557-573
◽
Keyword(s):
Let M be a finite monoid with unit group G. We consider a refinement, [Formula: see text] of the Green’s relation [Formula: see text]. The [Formula: see text]-classes, denoted [Formula: see text] are the G×G orbits, GHG, of the ℋ-classes, H, of M. With an orbit [Formula: see text] we associate a local monoid [Formula: see text] and determine the structure of these local monoids. The theory is applied to the full transformation semigroup [Formula: see text] and we see that the number of orbits [Formula: see text] in [Formula: see text] is equal to the number of partitions of n.
1998 ◽
Vol 57
(1)
◽
pp. 59-71
◽
2005 ◽
Vol 71
(1)
◽
pp. 69-74
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2016 ◽
Vol 09
(01)
◽
pp. 1650042
2008 ◽
Vol 78
(1)
◽
pp. 117-128
◽
2013 ◽
Vol 12
(08)
◽
pp. 1350041
◽
2012 ◽
Vol 05
(03)
◽
pp. 1250035
◽
1967 ◽
Vol 15
(3)
◽
pp. 233-240
◽
2018 ◽
Vol 2018
◽
pp. 1-9