Implicative hyper K -algebras

Mohammad Mehdi Zahedi; A. Borumand Saeid; R. A. Borzooei

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 2, page 439-453
  • ISSN: 0011-4642

Abstract

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In this note we first define the notions of (weak, strong) implicative hyper K -algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K -ideals. Also we obtain some relations between these notions and (weak) implicative hyper K -ideals. Finally, we study the implicative hyper K -algebras of order 3, in particular we obtain a relationship between the positive implicative hyper K -algebras and (weak, strong) implicative hyper K -algebras under a simple condition.

How to cite

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Zahedi, Mohammad Mehdi, Saeid, A. Borumand, and Borzooei, R. A.. "Implicative hyper $K$-algebras." Czechoslovak Mathematical Journal 55.2 (2005): 439-453. <http://eudml.org/doc/30957>.

@article{Zahedi2005,
abstract = {In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition.},
author = {Zahedi, Mohammad Mehdi, Saeid, A. Borumand, Borzooei, R. A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {hyper $K$-algebra; hyper $K$-ideal; (weak; strong) implicative hyper $K$-algebras; (weak) implicative hyper $K$-ideal; hyper -algebra; hyper -ideal; (weak, strong) implicative hyper -algebras; (weak) implicative hyper -ideal},
language = {eng},
number = {2},
pages = {439-453},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Implicative hyper $K$-algebras},
url = {http://eudml.org/doc/30957},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Zahedi, Mohammad Mehdi
AU - Saeid, A. Borumand
AU - Borzooei, R. A.
TI - Implicative hyper $K$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 439
EP - 453
AB - In this note we first define the notions of (weak, strong) implicative hyper $K$-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper $K$-ideals. Also we obtain some relations between these notions and (weak) implicative hyper $K$-ideals. Finally, we study the implicative hyper $K$-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper $K$-algebras and (weak, strong) implicative hyper $K$-algebras under a simple condition.
LA - eng
KW - hyper $K$-algebra; hyper $K$-ideal; (weak; strong) implicative hyper $K$-algebras; (weak) implicative hyper $K$-ideal; hyper -algebra; hyper -ideal; (weak, strong) implicative hyper -algebras; (weak) implicative hyper -ideal
UR - http://eudml.org/doc/30957
ER -

References

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  7. Sur une generalization de la notion de groups, 8th Congress Math. Scandinaves, Stockholm, 1934, pp. 45–49. (1934) 
  8. B C K -Algebras, Kyung Moonsa, Seoul, 1994. (1994) MR1297121
  9. M V -algebras are categorically equivalent to bounded commutative B C K -algebras, Math. Japon. 31 (1986), 889–894. (1986) Zbl0633.03066MR0870978
  10. Some classification of hyper K -algebras of order  3, Scientiae Mathematicae Japonicae 53 (2001), 133–142. (2001) MR1821608
  11. Some results on hyper K -algebra, Scientiae Mathematicae 3 (2000), 53–59. (2000) MR1758830

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