Mathematica Bohemica

Mathematica Bohemica, Vol. 149, No. 1, pp. 105-127, 2024

New kinds of hybrid filters of EQ-algebras

Akbar Paad

Received March 31, 2022. Published online March 21, 2023.

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.

Keywords: EQ-algebra; hybrid positive implicative (pre)filter; hybrid implicative (pre)filter

Classification MSC: 03G25, 03B50, 08A72, 03E72

DOI: 10.21136/MB.2023.0049-22

PDF available at: Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Akbar Paad, Department of Mathematics, University of Bojnord, University of Bojnord Rd, C7PW+8M3 Bojnord, Iran, e-mail: akbar.paad@gmail.com

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