Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 1
On Derivations and Lie Ideals of Semirings
Authors:
Madhu Dadhwal Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

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and
Neelam Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

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Pages:
81–99
Online Publication Date:
14 Apr 2022
Publication Date:
26 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2022.00011
Keywords (English):
semirings; Lie ideals; additively regular semirings; derivations; inner derivations and pseudo inverses
Open access

In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d 1 and d 2 of a prime semiring S with char S ≠ 2 and x d 1 x d 2 = 0, for all x ∈ S implies either d 1 = 0 or d 2 = 0.

  • [1]

    Albas, E. and Argac, N. Generalized derivations of prime rings. Algebra Colloquium 11, 3 (2004), 399–410.

  • [2]

    Argac, N. On prime and semiprime rings with derivations. Algebra Colloquium 13, 3 (2006), 371–380.

  • [3]

    Bandelt, H. J. and Petrich, M. Subdirect products of rings and distributive lattices. Proc. Edin Math. Soc. 25, 2 (1982), 135–171.

  • [4]

    Bergen, J. and Herstein, I. N. and Kerr, J. W. Lie ideals and derivations of prime rings. J. Algebra 7, I (1981), 259–267.

  • [5]

    Bresar, M. Centralizing mappings and derivations in prime rings. J. Algebra 156 (1993), 385–394.

  • [6]

    Bresar, M. On skew-commuting mapping of rings. Bull. Austral. Math. Soc. 47 (1993), 291–296.

  • [7]

    Bresar, M. and Hvala, B. On additive maps of prime rings. Bull. Austral. Math. Soc. 51 (1995), 377–381.

  • [8]

    Bresar, M. and Miers, C. R. Strong commutativity preserving maps of semiprime rings. Canad. Math. Bull. 37, 4 (1994), 457–460.

  • [9]

    Bresar, M. and Vukman, J. Orthogonal derivations and an extension of a theorem of Posner. Radovi Math. 5 (1989), 237–246.

  • [10]

    Golan, J. S. Semirings and their applications. Kluwer Academic Publishers. Dordrecht 1999.

  • [11]

    Karvellas, P. H. Inversive semirings. J. Austral. Math. Soc. 18 (1974), 277–288.

  • [12]

    Mayne, J. H. Centralizing mappings of prime rings. Canad. Math. Bull. 27, 1 (1984), 122–126.

  • [13]

    Mayne, J. H. Centralizing automorphisms of Lie ideals in prime rings. Canad. Math. Bull. 35, 4 (1992), 510–514.

  • [14]

    Posner, E. C. Derivations in prime rings. Proc. Amer. Math. Soc. 8 (1957), 1093–1100.

  • [15]

    Shafiq, S. and Aslam, M. On Posner’s second theorem in additively inverse semirings. Hacet. J. Math. Stat. 48, 4 (2019), 996–1000.

  • [16]

    Sharma, R. P. and Madhu. On connes subgroups and graded semirings. Vietnam Journal of Mathematics 38, 3 (2010), 287–298.

  • [17]

    Sharma, R. P. and Sharma, R. and Madhu. Radicals of semirings. Asian-European Journal of Mathematics 13, 7 2020, 2050138 (16 pages).

  • [18]

    Sharma, R. P. and Sharma, R. and Madhu and Kar, S. On the prime decomposition of k-ideals and fuzzy k-ideals in semirings. Fuzzy information and Engineering 13, 2 (2021), 223–235.

    • Search Google Scholar
    • Export Citation
  • [19]

    Sharma, R. P. and Sharma, T. R. and Joseph, R. Primary ideals in non-commutative semirings. Southeast Asian Bulletin of Mathematics (Springer-Verlag) 35, 2 (2011), 345–360.

    • Search Google Scholar
    • Export Citation
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Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
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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

  • Attila BÉRCZES (University of Debrecen)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • György DÓSA (University of Pannonia, Veszprém)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Gábor NYUL (University of Debrecen)
  • Margit PAP (University of Pécs)
  • István PINK (University of Debrecen)
  • 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
  • György GÁT (University of Debrecen)

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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
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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