Relative co-annihilators in lattice equality algebras

Sogol Niazian; Mona Aaly Kologani; Rajab Ali Borzooei

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 4, page 585-602
  • ISSN: 0862-7959

Abstract

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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 ∨ -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.

How to cite

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Niazian, Sogol, Aaly Kologani, Mona, and Borzooei, Rajab Ali. "Relative co-annihilators in lattice equality algebras." Mathematica Bohemica 149.4 (2024): 585-602. <http://eudml.org/doc/299627>.

@article{Niazian2024,
abstract = {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.},
author = {Niazian, Sogol, Aaly Kologani, Mona, Borzooei, Rajab Ali},
journal = {Mathematica Bohemica},
keywords = {equality algebra; annihilator; co-annihilator; relative co-annihilator; filter},
language = {eng},
number = {4},
pages = {585-602},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relative co-annihilators in lattice equality algebras},
url = {http://eudml.org/doc/299627},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Niazian, Sogol
AU - Aaly Kologani, Mona
AU - Borzooei, Rajab Ali
TI - Relative co-annihilators in lattice equality algebras
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 4
SP - 585
EP - 602
AB - 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.
LA - eng
KW - equality algebra; annihilator; co-annihilator; relative co-annihilator; filter
UR - http://eudml.org/doc/299627
ER -

References

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