• Title/Summary/Keyword: polygroup

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ON POLYGROUP HYPERRINGS AND REPRESENTATIONS OF POLYGROUPS

  • Davvaz, B.;Poursalavati, N.S.
    • Journal of the Korean Mathematical Society
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    • v.36 no.6
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    • pp.1021-1031
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    • 1999
  • In this paper we introduce matrix representations of polygroups over hyperrings and show such representations induce representations of the fundamental group over the corresponding fundamental ring. We also introduce the notion of a polygroup hyperring generalizing the notion of a group ring. We establish homo-morphisms among various polygroup hyperrings.

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ELEMENTARY TOPICS ON WEAK POLYGROUPS

  • Davvaz, B.
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.1-8
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    • 2003
  • In this paper, we further develop the weak polygroup theory, we define quotient weak polygroup and then the fundamental homomorphism theorem of group theory is derived in the context of weak polygroups. Also, we consider the fundamental relation $\beta$$^{*}$ defined on a weak polygroup and define a functor from the category of all weak polygroups into the category of all fundamental groups.s.

DERIVATION AND ACTOR OF CROSSED POLYMODULES

  • Davvaz, Bijan;Alp, Murat
    • The Pure and Applied Mathematics
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    • v.25 no.3
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    • pp.203-218
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    • 2018
  • An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.