Geodesic
New kinds of hybrid filters of EQ-algebras
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 105-127
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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.
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.
DOI : 10.21136/MB.2023.0049-22
Classification : 03B50, 03E72, 03G25, 08A72
Keywords: EQ-algebra; hybrid positive implicative (pre)filter; hybrid implicative (pre)filter 
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Paad, Akbar. New kinds of hybrid filters of EQ-algebras. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 105-127. doi: 10.21136/MB.2023.0049-22

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