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The finite basis problem for Kiselman monoids

Ashikhmin D. N., Volkov M. V., Zhang W. T.

Demonstratio Mathematica

2015

Vol. 48, nr 4

475--492

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke–Kiselman monoids including the Kiselman monoids Kn. As a consequence, we conclude that the identities of Kn are nonfinitely based for every n≥4 and exhibit a finite identity basis for the identities of each of the monoids K2 and K3.

Submonoids of generalized hypersubstitutions

Leeratanavalee S.

Demonstratio Mathematica

2007

Vol. 40, nr 1

13-22

In this paper we define the operation G on the set of all generalized hypersubstitutions and investigate some algebraic-structural properties of the set of all generalized hypersubstitutions and of some submonoids M of the set of all generalized hypersubstitutions, respectively.

Note on logics of idempontents

Katrnoška F.

Demonstratio Mathematica

2004

Vol. 37, nr 2

267--274

The main result of this paper is the characterization of certain logics of idempotents by Boolean semirings. Moreover some interesting examples are likewise added.

The generalized residue classes and integral monoids with minimal sets

Rycerz A.

Opuscula Mathematica

2000

Vol. 20

65-69

In this note we consider the integral monoids mon(A) = {Ax : x ∈ Zn+}, where A ∈ Zmxn, with the swelling points. Such monoids appear in the natural way in the generalized Frobenius problem in Zm. An integral element g ∈ mon(A) is called the swelling point if (g + cone(A)) ∩ Zm ⊆ mon(A), where cone(A) = {Ax : x ∈ Rn+}. The aim of this note is to characterize the structure of the set of swelling points in terms of the generalized residue classes.

W pracy rozważane są całkowite monoidy mon(A) = {Ax : x ∈ Zn+}, gdzie A ∈ Zmxn, z punktami źródłowymi, które w naturalny spo sób pojawiają się przy próbach uogólniania jednowymiarowego problemu Frobeniusa na przypadek wielowymiarowy. Punkt g ∈ mon(A) jest punktem źródłowym, jeśli (g + cone(A)) ∩ Zm ⊆ mon(A), gdzie cone(A) = {Ax : x ∈ Rn+}. Głównym rezultatem pracy jest charakteryzacja struktury zbioru punktów źródłowych za pomocą uogólnionych klas reszt.