Fundamental hoop-algebras

R.A. Borzooei, H.R. Varasteh, K. Borna

Abstract


In this paper, we investigate some results on hoop algebras and hyper hoop-algebras. We construct a hoop and a hyper hoop on any countable set. Then using the notion of the fundamental relation we define the fundamental hoop and we show that any hoop is a fundamental hoop and then we construct a fundamental hoop on any non-empty countable set.


Keywords


hoop algebras, hyper hoop algebras, (strong) regular rela- tion,fundamental relations.

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References


P. Aglianò, I.M.A. Ferreirim, F. Montagna, Basic hoops: an algebraic study of continuous t-norms, Studia Logica, 87(1) (2007), 73-98.

W.J. Blok, I.M.A. Ferreirim, Hoops and their implicational reducts, Algebraic Methods in Logic and Computer Science, Banach Center Publications, 28 (1993), 219-230.

W.J. Blok, I.M.A. Ferreirim, On the structure of hoops, Algebra Universalis, 43 (2000), 233-257.

R.A. Borzooei, Hyper BCK and K-algebras, Ph.D. Thesis, Shahid Bahonar University of Kerman, (2000).

R.A. Borzooei, H. Rezaei, M.M. Zahedi, Classifications of hyper BCK-algebras of order 3, Italian Journal of Pure and Applied Mathematics, 12 (2002), 175-184.

R.A. Borzooei, H.R.Varasteh, K. Borna, Quotient hyper hoop algebras, Italian Journal of Aure and applied Mathematics, 36 (2016), 87-100.

B. Bosbach, Komplementare halbgruppen. Axiomatik und arithmetik, Fundamenta Mathematicae, Vol. 64 (1969), 257-287.

J.R. Büchi, T.M. Owens, Complemented monoids and hoops, Unpublished manuscript.

P. Corsini, V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, (2003).

P. Corsini,Prolegomena of Hypergroup Theory. Aviani Editore Tricesimo, (1993).

Sh. Ghorbani, A. Hasankhani, E. Eslami, Quotient hyper MV-algebras, Scientiae Mathematicae Japonicae Online, (2007), 521-536.

Sh. Ghorbani, A. Hasankhani, E. Eslami, Hyper MV-algebras, Set-Valued Math, Appl, 1, (2008), 205-222.

P. Hájek, Metamathematics of fuzzy logic, Trends in Logic-Studia Logica Library, Dordrecht/Boston/London,(1998).

P.R. Halmos, Naive Set Theory, Springer-Verlag, New York, (1974).

F. Marty, Sur une generalization de la notion de groupe, 8 th Congress Mathematiciens Scan- dinaves, Stockholm, (1934), 45-49.

H.R. Varasteh, R.A. Borzooei, Fuzzy regular relation on hyper hoops, Journal of Intelligent and Fuzzy Systems, 30 (2016), 12751282.

M.M. Zahedi, R.A. Borzooei, H. Rezaei, Some Classifications of Hyper K-algebras of order 3, Scientiae Mathematicae Japonicae, 53(1) (2001), 133-142.




DOI: http://dx.doi.org/10.23755/rm.v29i1.20

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