New kinds of hybrid filters of EQ-algebras

Akbar Paad

Mathematica Bohemica (2024)

  • Issue: 1, page 105-127
  • ISSN: 0862-7959

Abstract

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The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is shown that these concepts coincide in good involutive EQ-algebras. Finally, it is proved that the quotient EQ-algebra respect to a hybrid positive implicative filter is involutive if and only if the hybrid filter is hybrid implicative filter.

How to cite

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Paad, Akbar. "New kinds of hybrid filters of EQ-algebras." Mathematica Bohemica (2024): 105-127. <http://eudml.org/doc/299244>.

@article{Paad2024,
abstract = {The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is shown that these concepts coincide in good involutive EQ-algebras. Finally, it is proved that the quotient EQ-algebra respect to a hybrid positive implicative filter is involutive if and only if the hybrid filter is hybrid implicative filter.},
author = {Paad, Akbar},
journal = {Mathematica Bohemica},
keywords = {EQ-algebra; hybrid positive implicative (pre)filter; hybrid implicative (pre)filter},
language = {eng},
number = {1},
pages = {105-127},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New kinds of hybrid filters of EQ-algebras},
url = {http://eudml.org/doc/299244},
year = {2024},
}

TY - JOUR
AU - Paad, Akbar
TI - New kinds of hybrid filters of EQ-algebras
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 105
EP - 127
AB - The main goal of this paper is to introduce hybrid positive implicative and hybrid implicative (pre)filters of EQ-algebras. In the following, some characterizations of this hybrid (pre)filters are investigated and it is proved that the quotient algebras induced by hybrid positive implicative filters in residuated EQ-algebras are idempotent and residuated EQ-algebra. Moreover, the relationship between hybrid implicative prefilters and hybrid positive implicative prefilters are discussed and it is shown that these concepts coincide in good involutive EQ-algebras. Finally, it is proved that the quotient EQ-algebra respect to a hybrid positive implicative filter is involutive if and only if the hybrid filter is hybrid implicative filter.
LA - eng
KW - EQ-algebra; hybrid positive implicative (pre)filter; hybrid implicative (pre)filter
UR - http://eudml.org/doc/299244
ER -

References

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