Gröbner-Shirshov Bases of Some Semigroup Constructions

Karpuz, Eylem Güzel

doi:10.1142/s100538671500005x

Cited by 8 publications

(4 citation statements)

References 30 publications

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“…Another future work for flows monoid is to present a Gröbner-Shirshov basis for each example in this paper. We may refer to [9][10][11][12][13] for more details.…”

Section: Flows On Cauchy Categoriesmentioning

confidence: 99%

Flows on Classes of Regular Semigroups and Cauchy Categories

Wazzan

2019

Journal of Mathematics

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We consider the structure of the flow monoid for some classes of regular semigroups (which are special case of flows on categories) and for Cauchy categories. In detail, we characterize flows for Rees matrix semigroups, rectangular bands, and full transformation semigroups and also describe the Cauchy categories for some classes of regular semigroups such as completely simple semigroups, Brandt semigroups, and rectangular bands. In fact, we obtain a general structure for the flow monoids on Cauchy categories.

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“…Another future work for flows monoid is to present a Gröbner-Shirshov basis for each example in this paper. We may refer to [9][10][11][12][13] for more details.…”

Section: Flows On Cauchy Categoriesmentioning

confidence: 99%

Flows on Classes of Regular Semigroups and Cauchy Categories

Wazzan

2019

Journal of Mathematics

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“…Yarıgrup Teorisinde bir yarıgrubun (monoidin) bir sonlu yarıgrup (monoid) takdimini bulmak ve üstelik monoidlerin Bruck-Reilly genişlemelerinin özelliklerini incelemek önemli bir çalışma alanıdır ve literatürde uzun yıllardır çalışılır (örneğin, Araujo and Ruskuc 2001, Carvalho 2006, Carvalho 2007, Karpuz 2015, Yamamura 2001.…”

Section: Introductionunclassified

Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi

Yağcı

2024

Afyon Kocatepe University Journal of Sciences and Engineering

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M bir monoid ve θ, M üzerinde bir endomorfizm olsun. N^0 negatif olmayan tamsayıların kümesi, r=max{n,p} ve θ^0, M üzerinde birim dönüşüm olmak üzere N^0×M×N^0 kümesi (m,a,n)(p,b,q)=(m-n+r,(aθ^(r-n) ) (bθ^(r-p) ),q-p+r) ikili işlemi ile birlikte bir monoid tanımlar. Bu monoide θ nin belirlediği M nin Bruck-Reilly genişlemesi denir ve BR(M,θ) ile gösterilir. Bu çalışmada, bir sonlu M monoidinin Bruck-Reilly genişlemesinin ikinci tamsayı homolojisinin, öyle bir k∈N için H_2 (BR(M,θ))=H_2 (M)×Z^k olduğu gösterilmiştir.

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“…There are some important studies on this subject related to the groups (see, for instance, [7,11]). We may finally refer the papers [2,3,8,[14][15][16][17] for some other recent studies over Gröbner- Shirshov bases. Algorithmic problems such as the word, conjugacy and isomorphism problems have played an important role in group theory since the work of M. Dehn in early 1900's. These problems are called decision problems which ask for a yes or no answer to a specific question.…”

Section: Introductionmentioning

confidence: 99%

A solution of the word problem for braid groups via the complex reflection group G12

Çevik

Albargi

2020

Filomat

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It is known that if there exists a Gr?bner-Shirshov basis for a group G, then we say that one of the decision problem, namely the word problem, is solvable for G as well. Therefore, as the main target of this paper, we will present a (non-commutative) Gr?bner-Shirshov basis for the braid group associated with the congruence classes of complex reflection group G12 which will give us normal forms of the elements of G12 and so will obtain a new algorithm to solve the word problem over it.

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Gröbner-Shirshov Bases of Some Semigroup Constructions

Abstract: In this paper, we obtain (non-commutative) Gröbner-Shirshov bases for rectangular bands, small extensions of semigroups and Bruck-Reilly extensions of monoids in terms of the general product.

Cited by 8 publications

References 30 publications

Flows on Classes of Regular Semigroups and Cauchy Categories

Flows on Classes of Regular Semigroups and Cauchy Categories

Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi

A solution of the word problem for braid groups via the complex reflection group G12

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