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International Journal of Algebra and Computation, 2004
This contribution wishes to argue in favor of increased interaction between experts on finite monoids and specialists of theory of computation. Developing the algebraic approach to formal computations as well as the computational point of view on monoids will prove to be beneficial to both communities.
Pascal Tesson, Denis Thérien
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This contribution wishes to argue in favor of increased interaction between experts on finite monoids and specialists of theory of computation. Developing the algebraic approach to formal computations as well as the computational point of view on monoids will prove to be beneficial to both communities.
Pascal Tesson, Denis Thérien
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Semigroup Forum, 2002
The authors introduce and investigate a new class of monoids, called finitary monoids (here monoid means a commutative, cancellative semigroup with identity element). A monoid \(H\) (written multiplicatively) with group of invertible elements \(H^\times\) is called finitary if there is a finite subset \(U\subset H- H^\times\) such that \((H-H^\times)^n\
Geroldinger, Alfred +3 more
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The authors introduce and investigate a new class of monoids, called finitary monoids (here monoid means a commutative, cancellative semigroup with identity element). A monoid \(H\) (written multiplicatively) with group of invertible elements \(H^\times\) is called finitary if there is a finite subset \(U\subset H- H^\times\) such that \((H-H^\times)^n\
Geroldinger, Alfred +3 more
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Möbius monoids and their connection to inverse monoids
Semigroup Forum, 2014A monoid \(M\) satisfying the following conditions is called a \textit{Möbius monoid}: 1) \(M\) is decomposition-finite (i.e., for any \(a\in M\) there is a finite number of pairs \((b,c)\in M\times M\) such that \(a=bc\)); 2) \(ab=1\Rightarrow a=b=1\); 3) \(ab=b\Rightarrow a=1\). \(\mathfrak M\) denotes a non-trivial right cancellative left rigid (i.e.
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Monoids, Krull Monoids, Large Monoids
2019In this chapter, we review what we will need in the rest of the book as far as commutative monoids are concerned. This will show how much we assume of the reader. The contents of Sections 1.5 and 1.7 are exceptions: they are completely independent of the rest of the chapter.
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In this paper we introduce the notion of generalized factorization for an arbitrary submonoid M subset of A*, where A* is the free monoid generated by an alphabet A, generalizing, in this way, the notion of factorization of A*. Then we give a characterization of the free product of two submonoids of A* in terms of unambiguous products of monoids. To do
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Algebraic Monoids and Renner Monoids
2014We collect some necessary concepts and principles in the theory of linear algebraic monoids which apply to further investigation on other topics such as the classification of reductive monoids, representations of algebraic monoids, monoids of Lie type, cell decompositions, monoid Hecke algebra, and monoid schemes.
Zhenheng Li, Zhuo Li, You’an Cao
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On deciding whether a monoid is a free monoid or is a group
Acta Informatica, 1986Monoids which are described by a given finite presentation (\(\Sigma\) ;R), i.e. \(\Sigma\) is a finite alphabet and R is a finite string-rewriting system on \(\Sigma\), are considered. It is shown that the problem whether or not such a monoid is a free one or a group are undecidable in general.
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