Geodesic
Relative co-annihilators in lattice equality algebras
Mathematica Bohemica, Tome 149 (2024) no. 4, pp. 585-602 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $ \vee $-irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $ \mathcal {\mathbb {E}} $ and $ \mathbb {F} $ a filter of $ \mathcal {\mathbb {E}} $, we define the set of all $ \mathbb {F} $-involutive filters of $ \mathcal {\mathbb {E}} $ and show that by defining some operations on it, it makes a BL-algebra.
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 $ \vee $-irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $ \mathcal {\mathbb {E}} $ and $ \mathbb {F} $ a filter of $ \mathcal {\mathbb {E}} $, we define the set of all $ \mathbb {F} $-involutive filters of $ \mathcal {\mathbb {E}} $ and show that by defining some operations on it, it makes a BL-algebra.
DOI : 10.21136/MB.2024.0120-23
Classification : 03G10, 06B75, 06B99
Keywords: equality algebra; annihilator; co-annihilator; relative co-annihilator; filter 
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Niazian, Sogol; Aaly Kologani, Mona; Borzooei, Rajab Ali. Relative co-annihilators in lattice equality algebras. Mathematica Bohemica, Tome 149 (2024) no. 4, pp. 585-602. doi: 10.21136/MB.2024.0120-23

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