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Characterization of Additive (m, n)-Semihyperrings

  • MIRAKILI, SAEED (Department of Mathematics, Payame Noor University) ;
  • DAVVAZ, BIJAN (Department of Mathematics, Yazd University)
  • Received : 2013.11.09
  • Accepted : 2014.08.21
  • Published : 2015.09.23

Abstract

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.

Keywords

hypergroup;hyperring;additive (m, n)-semihyperring;hyperideal;strongly regular relation

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