The Journal of Pedagogical University of Cracow

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Annales Uni. P. Cr. St. M.

<abstract>
<title style='display:none'>Abstract</title>
In this paper we continue our investigation concerning the concept of a <italic>liken</italic>. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in ℝ. The most important examples of likens are clearly the set of natural numbers ℕ with addition and the set of positive natural numbers ℕ* with multiplication, represented by the sequence <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2022-0007_eq_001.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>ln</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>∞</mml:mo></mml:msubsup></mml:mrow></mml:math>
<tex-math>\left( {\ln \left( {n + 1} \right)} \right)_{n = 0}^\infty</tex-math>
</alternatives>
</inline-formula>. The set of all likens can be parameterized by the points of some infinite dimensional, complete metric space. In this <italic>space of likens</italic> we consider elements up to isomorphism and define <italic>properties of likens</italic> as such that are isomorphism invariant. The main result of this paper is a theorem characterizing the liken ℕ* of natural numbers with multiplication in the space of all likens.
</abstract>

Abstract

Department of Mathematics and Computer Science

Department of Mathematics and Natural Sciences

Keywords

<article-title>On a certain characterisation of the semigroup of positive natural numbers with multiplication</article-title>

On a certain characterisation of the semigroup of positive natural numbers with multiplication

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica ist in den folgenden Services indiziert: <UL> <LI>Arianta </LI> <LI>Baidu Scholar </LI> <LI>CNKI Scholar (China National Knowledge Infrastructure) </LI> <LI>CNPIEC - cnpLINKer </LI> <LI>Dimensions </LI> <LI>DOAJ (Directory of Open Access Journals) </LI> <LI>EBSCO </LI> <LI>ExLibris </LI> <LI>Google Scholar </LI> <LI>Index Copernicus </LI> <LI>Japan Science and Technology Agency (JST) </LI> <LI>J-Gate </LI> <LI>JournalGuide </LI> <LI>JournalTOCs </LI> <LI>KESLI-NDSL (Korean National Discovery for Science Leaders) </LI> <LI>Mathematical Reviews (MathSciNet) </LI> <LI>MyScienceWork </LI> <LI>Naver Academic </LI> <LI>Naviga (Softweco) </LI> <LI>QOAM (Quality Open Access Market) </LI> <LI>ReadCube </LI> <LI>SCILIT </LI> <LI>Semantic Scholar </LI> <LI>Sherpa/RoMEO </LI> <LI>TDNet </LI> <LI>The Polish Digital Mathematical Library (DML-PL) </LI> <LI>Ulrich's Periodicals Directory/ulrichsweb </LI> <LI>WanFang Data </LI> <LI>Web of Science - Emerging Sources Citation Index </LI> <LI>WorldCat (OCLC) </LI> <LI>X-MOL </LI> <LI>zbMATH Open </LI></UL>

Editor-in-Chief Paweł Wójcik, Pedagogical University of Krakow, Poland Editors and Editorial Advisory Board Wojciech Chachólski, Royal Institute of Technology, KTH, Sweden Márton Elekes, Hungarian Academy of Sciences, Hungary Beata Gryszka, Pedagogical University of Krakow, Poland (secretary) Karol Gryszka, Pedagogical University of Krakow, Poland (secretary) Giovanna Ilardi, Università degli studi di Napoli ’’Federico II”, Italy Alex Küronya, Budapest University of Technology and Economics, Hungary Mohammad Sal Moslehian, Ferdowsi University of Mashhad, Iran Zsolt Páles, University of Debrecen, Hungary Tomasz Szemberg, PedagoPedagogical University of Krakow, Poland Justyna Szpond, Pedagogical University of Krakow, Poland Behrouz Taji, Albert Ludwigs University of Freiburg, Germany Technical Editors Paweł Pasteczka, Pedagogical University of Krakow, Poland Paweł Solarz, Pedagogical University of Krakow, Poland Contact <A href="mailto:studmath@up.krakow.pl">studmath@up.krakow.pl</A> Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland T: +48 22 701 50 15

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<DIV align=left> Scope and AIM Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica (AUPC SM) publishes high quality original papers on new methods and results that hold prospect for substantial progress in mathematics. Our scope focuses on the following branches of the contemporary mathematics, namely analysis, algebra, combinatorics, geometry, number theory, and topology. However, we can also consider for publication high quality papers from other subjects that could potentially have a significant impact on the development of mathematics. We also accept well-written survey and expository papers. Short announcements on future results are not accepted. The Editorial Board expects high standards of submissions; we look for articles that inform, stimulate, challenge, or even enlighten. Novelty, clarity of exposition, and broad appeal lies in the priority of the journal. Appropriate figures, tables, and diagrams are strongly encouraged. Quick and fair processing of all submissions is our priority. All submitted papers undergo a refereeing procedure by an international board whose members represent a wide spectrum of research interests. Publication in Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica is free of charge (Diamond Open Access -- free to read and free to publish). Volumes I-VII appeared as Annales Academiae Paedagogicae Cracoviensis Studia Mathematica. Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism Policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. Target Group - researchers in all branches of pure mathematics</DIV>

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

On a certain characterisation of the semigroup of positive natural numbers with multiplication

Edward Tutaj
Edward Tutaj

Online veröffentlicht: 08 Dec 2022

Volumen & Heft: Volumen 21 (2022) - Heft 1 (January 2022)

Seitenbereich: 71 - 92

Eingereicht: 09 May 2022

Akzeptiert: 05 Oct 2022

Details zu Zeitschrift und Ausgabe

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

On a certain characterisation of the semigroup of positive natural numbers with multiplication

Edward TutajEdward Tutaj

Online veröffentlicht: 08 Dec 2022

Volumen & Heft: Volumen 21 (2022) - Heft 1 (January 2022)

Seitenbereich: 71 - 92

Eingereicht: 09 May 2022

Akzeptiert: 05 Oct 2022

Details zu Zeitschrift und Ausgabe

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

PDF-Vorschau

Referenzen

Neueste Artikel

Edward Tutaj
Edward Tutaj