The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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DERIVATION AND ACTOR OF CROSSED POLYMODULES

  • Davvaz, Bijan (Department of Mathematics, Yazd University) ;
  • Alp, Murat (Department of Mathematics, American University of the Middle East)
  • Received : 2018.05.24
  • Accepted : 2018.07.30
  • Published : 2018.08.31
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Abstract

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.

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References

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