scholarly journals An element of a finite monoid is right invertible if and only if it is left invertible

2020 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Finite Monoid

We prove the proposition addressed in the title of this paper.

A NEW PROOF OF SCHUTZENBERGER'S THEOREM

2000 ◽  
Vol 10 (02) ◽  
pp. 217-220 ◽  
Author(s):  
PETER M. HIGGINS
Keyword(s):  
Finite Automata ◽  
Forward Direction ◽  
Regular Languages ◽  
Finite Monoid

We prove the theorem of Schutzenberger that a language is star-free if and only if it is recognized by a finite monoid with trivial subgroups. The forward direction follows the lines of the proof of Kleene's Theorem which characterizes regular languages as those recognized by finite automata. The converse is a relatively short induction.

Regular Languages Definable by Lindström Quantifiers (Preliminary Version)

2002 ◽  
Vol 9 (20) ◽  
Author(s):  
Zoltán Ésik ◽  
Kim G. Larsen
Keyword(s):  
Semidirect Product ◽  
Expressive Power ◽  
Regular Languages ◽  
Finite Monoid ◽  
Preliminary Version

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoid-generator pairs. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.<br /><br />Superseded by BRICS-RS-03-28.

THE ORBIT STRUCTURE OF FINITE MONOIDS

1993 ◽  
Vol 03 (04) ◽  
pp. 557-573 ◽  
Author(s):  
ROB CARSCADDEN
Keyword(s):  
Transformation Semigroup ◽  
Unit Group ◽  
Full Transformation ◽  
Finite Monoid ◽  
Orbit Structure ◽  
Finite Monoids ◽  
Full Transformation Semigroup ◽  
Green’S Relation

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.

scholarly journals R-POLYNOMIALS OF FINITE MONOIDS OF LIE TYPE

2010 ◽  
Vol 20 (06) ◽  
pp. 793-805 ◽  
Author(s):  
KÜRŞAT AKER ◽  
MAHIR BILEN CAN ◽  
MÜGE TAŞKIN
Keyword(s):  
Weyl Group ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Möbius Function ◽  
Necessary Condition ◽  
Finite Monoid ◽  
Finite Monoids ◽  
Mobius Function ◽  
Renner Monoid

This paper studies the combinatorics of the orbit Hecke algebras associated with W × W orbits in the Renner monoid of a finite monoid of Lie type, M, where W is the Weyl group associated with M. It is shown by Putcha in [12] that the Kazhdan–Lusztig involution [6] can be extended to the orbit Hecke algebra which enables one to define the R-polynomials of the intervals contained in a given orbit. Using the R-polynomials, we calculate the Möbius function of the Bruhat–Chevalley ordering on the orbits. Furthermore, we provide a necessary condition for an interval contained in a given orbit to be isomorphic to an interval in some Weyl group.

scholarly journals The Coarse Structure of the Representation Algebra of a Finite Monoid

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mary Schaps
Keyword(s):  
Fine Structure ◽  
Finite Monoid ◽  
Coarse Structure ◽  
Primitive Idempotents ◽  
Complete Set ◽  
One To One ◽  
Representation Algebra

Let M be a monoid, and let L be a commutative idempotent submonoid. We show that we can find a complete set of orthogonal idempotents L^0 of the monoid algebra A of M such that there is a basis of A adapted to this set of idempotents which is in one-to-one correspondence with elements of the monoid. The basis graph describing the Peirce decomposition with respect to L^0 gives a coarse structure of the algebra, of which any complete set of primitive idempotents gives a refinement, and we give some criterion for this coarse structure to actually be a fine structure, which means that the nonzero elements of the monoid are in one-to-one correspondence with the vertices and arrows of the basis graph with respect to a set of primitive idempotents, with this basis graph being a canonical object.

scholarly journals SOLVABLE MONOIDS WITH COMMUTING IDEMPOTENTS

2005 ◽  
Vol 15 (03) ◽  
pp. 547-570 ◽  
Author(s):  
MANUEL DELGADO ◽  
VÍTOR H. FERNANDES
Keyword(s):  
Finite Group ◽  
Solvable Group ◽  
Finite Monoid ◽  
Derived Subgroup ◽  
Abelian Kernel ◽  
A Finite Group

The notion of Abelian kernel of a finite monoid extends the notion of derived subgroup of a finite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idempotents. We prove in this paper that the finite idempotent commuting monoids satisfying this property are precisely those whose subgroups are solvable.

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