A BISIMPLE INVERSE MONOID OF QUADRUPLES OF NON-NEGATIVE INTEGERS. THE MÖBIUS FUNCTION.
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| Title: | A BISIMPLE INVERSE MONOID OF QUADRUPLES OF NON-NEGATIVE INTEGERS. THE MÖBIUS FUNCTION. |
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| Authors: | SCHWAB, EMIL DANIEL1 eschwab@utep.edu |
| Source: | Discussiones Mathematicae: General Algebra & Applications. 2024, Vol. 44 Issue 1, p111-126. 16p. |
| Subjects: | Möbius function, Integers, Monoids |
| Abstract: | The additive monoid of non-negative integers ℕ is isomorphic to the right unit submonoid of the (bisimple) bicyclic semigroup B = ℕ x ℕ. The aim of this note is to construct a similar pair of monoids (B = ℕ x ℕ, B = ℕ x ℕ x ℕ x ℕ). The monoid B gives rise to a bisimple inverse monoid B of quadruples of non-negative integers like as Warne 's 2-dimensional bicyclic semigroup. The links with the monoid of non-negative integers ℕ and with the bicyclic semigroup may turn out to be expedient also for the computation of the corresponding Möbius functions. [ABSTRACT FROM AUTHOR] |
| Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 177932186 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A BISIMPLE INVERSE MONOID OF QUADRUPLES OF NON-NEGATIVE INTEGERS. THE MÖBIUS FUNCTION. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22SCHWAB%2C+EMIL+DANIEL%22">SCHWAB, EMIL DANIEL</searchLink><relatesTo>1</relatesTo><i> eschwab@utep.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discussiones+Mathematicae%3A+General+Algebra+%26+Applications%22">Discussiones Mathematicae: General Algebra & Applications</searchLink>. 2024, Vol. 44 Issue 1, p111-126. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Möbius+function%22">Möbius function</searchLink><br /><searchLink fieldCode="DE" term="%22Integers%22">Integers</searchLink><br /><searchLink fieldCode="DE" term="%22Monoids%22">Monoids</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The additive monoid of non-negative integers ℕ is isomorphic to the right unit submonoid of the (bisimple) bicyclic semigroup B = ℕ x ℕ. The aim of this note is to construct a similar pair of monoids (B = ℕ x ℕ, B = ℕ x ℕ x ℕ x ℕ). The monoid B gives rise to a bisimple inverse monoid B of quadruples of non-negative integers like as Warne 's 2-dimensional bicyclic semigroup. The links with the monoid of non-negative integers ℕ and with the bicyclic semigroup may turn out to be expedient also for the computation of the corresponding Möbius functions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.7151/dmgaa.1440 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 111 Subjects: – SubjectFull: Möbius function Type: general – SubjectFull: Integers Type: general – SubjectFull: Monoids Type: general Titles: – TitleFull: A BISIMPLE INVERSE MONOID OF QUADRUPLES OF NON-NEGATIVE INTEGERS. THE MÖBIUS FUNCTION. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: SCHWAB, EMIL DANIEL IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 15099415 Numbering: – Type: volume Value: 44 – Type: issue Value: 1 Titles: – TitleFull: Discussiones Mathematicae: General Algebra & Applications Type: main |
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