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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Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

Edward Tutaj
Edward Tutaj

Data publikacji: 08 Dec 2022

Tom & Zeszyt: Tom 21 (2022) - Zeszyt 1 (January 2022)

Zakres stron: 71 - 92

Otrzymano: 09 May 2022

Przyjęty: 05 Oct 2022

Dziennik i szczegóły wydania

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Podgląd PDF

Referencje

Najnowsze artykuły

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

Edward TutajEdward Tutaj

Data publikacji: 08 Dec 2022

Tom & Zeszyt: Tom 21 (2022) - Zeszyt 1 (January 2022)

Zakres stron: 71 - 92

Otrzymano: 09 May 2022

Przyjęty: 05 Oct 2022

Dziennik i szczegóły wydania

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Podgląd PDF

Referencje

Najnowsze artykuły

Edward Tutaj
Edward Tutaj