Affiliations: Department of Mathematics, Shahid Beheshti University, Tehran, Iran | Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland | Department of Mathematics, Payam Noor University, Tehran, Iran
Note: [] Corresponding author. W.A. Dudek, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland. Fax. +48 71 320 07 51; E-mails: wieslaw.dudek@pwr.edu.pl (W.A. Dudek); borzooei@sbu.ac.ir (R.A. Borzooei), ateferadfar@yahoo.com (A. Radfar), om.zahiri@gmail.com (O. Zahiri).
Abstract: We describe relations between hyper MV-algebras and hyper K-algebras and prove that a finite hyper MV-algebra satisfying the condition $0\CirclePlus x = \{x\}$, used by many authors, is in fact an ordinary MV-algebra. We also characterize relations between the main types of deductive systems of hyper MV-algebras.
Keywords: (proper) hyper MV-algebra, hyper K-algebra, deductive system
