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On ideal theory of hoops

Mona Aaly Kologani;  Rajab Ali Borzooei — 2020

Mathematica Bohemica

In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a ∨ -hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship...

Relative co-annihilators in lattice equality algebras

Sogol Niazian;  Mona Aaly Kologani;  Rajab Ali Borzooei — 2024

Mathematica Bohemica

We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among ∨ -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra 𝔼 and 𝔽 a filter of 𝔼 , we define the set of all 𝔽 -involutive filters of 𝔼 and show that by defining some operations on it, it makes a BL-algebra.

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