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On Automatic Rees Matrix Semigroups
"... We consider a Rees matrix semigroup S = M[U ; I; J ; P ] over a semigroup U , with I and J nite index sets, and relate the automaticity of S with the automaticity of U . We prove that if U is an automatic semigroup and S is nitely generated then S is an automatic semigroup. ..."
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We consider a Rees matrix semigroup S = M[U ; I; J ; P ] over a semigroup U , with I and J nite index sets, and relate the automaticity of S with the automaticity of U . We prove that if U is an automatic semigroup and S is nitely generated then S is an automatic semigroup.
Principal Ideal Graphs of Rees Matrix Semigroups
"... Let S be a finite regular semigroup. We define the principal left ideal graph of S as the graph SG with V (SG) = S and two vertices a and b (a = b) are adjacent in SG if and only if Sa ∩ Sb = {}. The principal right ideal graph is defined accordingly and is denoted by GS. The principal ideal grap ..."
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graph of Rees matrix semigroup is studied in this paper. First, we describe the necessary and sufficient condition for which two elements in a Rees matrix semigroup are adjacent in SG and GS. Then we characterise the principal ideal graphs of a Rees matrix semigroup. Finally we describe the number
THE LOOP PROBLEM FOR REES MATRIX SEMIGROUPS
, 2007
"... Abstract. We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zerosimple semigroups for which the loop problem is contextfree. We also establish ..."
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Abstract. We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zerosimple semigroups for which the loop problem is contextfree. We also establish
THE ALGEBRA OF ADJACENCY PATTERNS: REES MATRIX SEMIGROUPS WITH REVERSION
, 2009
"... We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by socalled adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the ..."
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We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by socalled adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties
Automatic Rees matrix semigroups over categories, arXiv: math.RA/0509313
, 2005
"... Abstract. We consider the preservation of the properties of automaticity and prefixautomaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the singleobject case of Rees matrix semigroups over semigroups. 1. ..."
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Abstract. We consider the preservation of the properties of automaticity and prefixautomaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the singleobject case of Rees matrix semigroups over semigroups. 1.
Complexity problems associated with matrix rings, matrix semigroups and Rees matrix semigroups
, 1997
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ON APPROXIMATE AMENABILITY OF REES SEMIGROUP ALGEBRAS
 ACTA UNIVERSITATIS APULENSIS
, 2011
"... Let S = M o (G, P, I) be a Rees matrix semigroup with zero over a group G, we show that the approximate amenability of ℓ 1 (S) is equivalent to its amenability whenever the group G is amenable and the index set I is finite. ..."
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Let S = M o (G, P, I) be a Rees matrix semigroup with zero over a group G, we show that the approximate amenability of ℓ 1 (S) is equivalent to its amenability whenever the group G is amenable and the index set I is finite.
ON THE EFFICIENCY AND DEFICIENCY OF REES MATRIX
"... Let S be a finite simple semigroup represented as a Rees matrix semigroup M[G; I, J; P] over a group G. We show that if G is efficient (i.e. if it can be defined by a presentation 〈 A  R 〉 with R  − A  = rank(H2(G))) then S is also efficient. We also show how to find a minimal presentation fo ..."
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Let S be a finite simple semigroup represented as a Rees matrix semigroup M[G; I, J; P] over a group G. We show that if G is efficient (i.e. if it can be defined by a presentation 〈 A  R 〉 with R  − A  = rank(H2(G))) then S is also efficient. We also show how to find a minimal presentation
Rees Matrix Covers and Semidirect Products of Regular Semigroups
, 1996
"... In a recent paper, P.G. Trotter and the author introduced a "regular" semidirect product UV of evarieties U and V. Among several specific situations investigated there was the case V = RZ, the evariety of right zero semigroups. Applying a covering theorem of McAlister, it was shown th ..."
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category SE and another in terms of S regularly dividing a regular Rees matrix semigroup over a member of U. The categorical condition leads directly to a characterization of the equality U RZ = LU in terms of a graphical condition on U, slightly weaker than `elocality'. Among consequences
Automatic structures for semigroup constructions
, 2008
"... We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, BruckReilly extensions and wreath products. 1 ..."
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We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, BruckReilly extensions and wreath products. 1
Results 1  10
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