Authors:
Tilak Raj Sharma Department of Mathematics, Himachal Pradesh University, Regional Centre Khaniyara, Dharamshala, Himachal Pradesh (India)-176218

Search for other papers by Tilak Raj Sharma in
Current site
Google Scholar
PubMed
Close
and
Hitesh Kumar Ranote Department of Mathematics, Himachal Pradesh University, Regional Centre Khaniyara, Dharamshala, Himachal Pradesh (India)-176218

Search for other papers by Hitesh Kumar Ranote in
Current site
Google Scholar
PubMed
Close
Open access

In this paper, we introduce the notion of a Gel’fand Γ-semiring and discuss the various characterization of simple, k-ideal, strong ideal, t-small elements and additively cancellative elements of a Gel’fand Γ-semiring R, and prove that the set of additively cancellative elements, set of all t-small elements of R and set of all maximal ideal of R are strong ideals. Further, let R be a simple Gel’fand Γ-semiring and 1 ≠ tR. Let M be the set of all maximal left (right) ideals of R. Then an element x of R is t-small if and only if it belongs to every maximal one sided left (right)ideal of R containing t.

  • [1]

    Barnes, W. E . On the Γ−rings of Nobusawa. Pacific J. Math. 18, 3 (1966), 411422.

  • [2]

    Dedekind, R . Über die Theorie der ganzen algebraischen Zahlen, supplement XI to P. G. Lejeune Dirichlet: Vorlesungen über Zahlentheorie. 4 Aufi., ch. Druck and Verlag, Braunschweig, 1894.

    • Search Google Scholar
    • Export Citation
  • [3]

    Eilenberg, S . Automata language and machines, vol. A. Academic Press, New York, 1974.

  • [4]

    Gel’fand, I . Normierte ringe. Mat. Sbornik 9 (1941), 323.

  • [5]

    Glazek, K . A guide to the literature on semiring and their applications in mathematics and information sciences. Kluwer Academic Publisher, Dordrecht, 2002.

    • Search Google Scholar
    • Export Citation
  • [6]

    Golan, J. S . Semirings and their applications. Kluwer Academic Publisher, Dordrecht/Boston/London, 1999.

  • [7]

    Golan, J. S . Semirings and affine equations over them: theory and application. Kluwer Academic Publisher, Dordrecht/Boston/London, 2003.

    • Search Google Scholar
    • Export Citation
  • [8]

    LaTorre, D. R . On h-ideals and k-ideals in hemirings. Publ. Math. Debrecen 12 (1965), 219226.

  • [9]

    Nobusawa, N . On a generalization of the ring theory. Osaka J. Math. 1 (1964), 8189.

  • [10]

    Rao, M. M. K . Γ-semirings-1. South East Asian Bull. of Math. 19 (1995), 4954.

  • [11]

    Rao, M. M. K . A study of bi-quasi-interior ideals as a new generalization of ideals of gen-eralization of semiring. Bulletin of The International Mathematical Virtual Institute 8 (2018), 519535.

    • Search Google Scholar
    • Export Citation
  • [12]

    Sharma, T. R . and Gupta, S . Some conditions on Γ-semirings. JCISS 41 (2016), 7987.

  • [13]

    Sharma, T. R . and Gupta, S . Ideals of a Bourne factor Γ-semirings. Proceedings of NCAMS-2016, Research Journal of Science and Technology 09, 01 (2017), 171174.

    • Search Google Scholar
    • Export Citation
  • [14]

    Sharma, T. R . and Ranote, H. K . More conditions on a Γ-semiring and ideals of an Izuka and Bourne factor Γ-Semiring. South East Asian Journal of Mathematics and Mathematical Sciences 18, 01 (April 2022), 7184.

    • Search Google Scholar
    • Export Citation
  • [15]

    Slowikowski, W . and Zawadowski, W . A generalization of maximal ideals method of stone and Gel’fand. Fund. Math. 42 (1995), 225231.

    • Search Google Scholar
    • Export Citation
  • [16]

    Vandiver, H. S . Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Amer. Math. Soc. 40, 12 (1934), 914920.

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation
1990
Volumes
per Year
1
Issues
per Year
2
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)