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Formations of orthodox semigroups 正统半群的形成

3区数学

Semigroup Forum Pub Date : 2023-11-08 DOI: 10.1007/s00233-023-10390-x

Gracinda M. S. Gomes, Ana-Catarina C. Monteiro

引用次数: 0

Homeomorphism groups on the positive real numbers defined by binary operations 由二元运算定义的正实数上的同胚群

3区数学

Semigroup Forum Pub Date : 2023-11-08 DOI: 10.1007/s00233-023-10395-6

Sin-Ei Takahasi

引用次数: 0

Equationally defined classes of semigroups 相等定义的半群类

3区数学

Semigroup Forum Pub Date : 2023-11-03 DOI: 10.1007/s00233-023-10397-4

Peter M. Higgins, Marcel Jackson

{"title":"Equationally defined classes of semigroups","authors":"Peter M. Higgins, Marcel Jackson","doi":"10.1007/s00233-023-10397-4","DOIUrl":"https://doi.org/10.1007/s00233-023-10397-4","url":null,"abstract":"Abstract We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra 555:131–156, 2020) that an elementary class $${mathscr {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also closed under the taking of containing semigroups, some basis of equations of $${mathscr {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> is free of the $$forall $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>∀</mml:mo> </mml:math> quantifier. We also observe the decidability of the class of equation systems satisfied by semigroups, via a link to systems of rationally constrained equations on free semigroups. Examples are given of EHP-classes for which neither $$(forall cdots )(exists cdots )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>∀</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mo>∃</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> equation systems nor $$(exists cdots )(forall cdots )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>∃</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mo>∀</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> systems suffice.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set 有限集上二面体逆单似体的三个显著子单似体的表示

3区数学

Semigroup Forum Pub Date : 2023-10-31 DOI: 10.1007/s00233-023-10396-5

Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro

引用次数: 0

An extension to “A subsemigroup of the rook monoid” “白嘴鸦单群的一个子半群”的推广

3区数学

Semigroup Forum Pub Date : 2023-10-19 DOI: 10.1007/s00233-023-10393-8

George Fikioris, Giannis Fikioris

{"title":"An extension to “A subsemigroup of the rook monoid”","authors":"George Fikioris, Giannis Fikioris","doi":"10.1007/s00233-023-10393-8","DOIUrl":"https://doi.org/10.1007/s00233-023-10393-8","url":null,"abstract":"Abstract A recent paper studied an inverse submonoid $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> of the rook monoid, by representing the nonzero elements of $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> via certain triplets belonging to $${mathbb {Z}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . In this note, we allow the triplets to belong to $${mathbb {R}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . We thus study a new inverse monoid $$overline{M}_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>n</mml:mi> </mml:msub> </mml:math> , which is a supermonoid of $$M_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> . We point out similarities and find essential differences. We show that $$overline{M}_{n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>n</mml:mi> </mml:msub> </mml:math> is a noncommutative, periodic, combinatorial, fundamental, completely semisimple, and strongly $${E}^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> -unitary inverse monoid.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The local bisection hypothesis for twisted groupoid C*-algebras 扭曲群C*-代数的局部等分假设

3区数学

Semigroup Forum Pub Date : 2023-10-17 DOI: 10.1007/s00233-023-10392-9

Becky Armstrong, Jonathan H. Brown, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge

引用次数: 0

The Frobenius problem for numerical semigroups generated by sequences of the form $$ca^n-d$$ 一类数列生成的数值半群的Frobenius问题 $$ca^n-d$$

3区数学

Semigroup Forum Pub Date : 2023-10-02 DOI: 10.1007/s00233-023-10387-6

Fabián Arias, Jerson Borja, Calixto Rhenals

引用次数: 0

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