Weak implicative filters in quasi-ordered residuated systems
Keyword(s):
The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure A = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters and implicative filters in this type of algebraic structures. In this article, the concept of weak implicative filters in a quasi-ordered residuated system is introduced as a continuation of previous researches. Also, some conditions for a filter of such system to be a weak implicative filter are listed.
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2021 ◽
Vol 35
◽
pp. 87-102
Keyword(s):
2020 ◽
Vol 9
(8)
◽
pp. 5683-5691
2021 ◽
Vol 1901
(1)
◽
pp. 012046
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