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

Voir la notice de l'article

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 
@article{10_21136_MB_2024_0120_23,
     author = {Niazian, Sogol and Aaly Kologani, Mona and Borzooei, Rajab Ali},
     title = {Relative co-annihilators in lattice equality algebras},
     journal = {Mathematica Bohemica},
     pages = {585--602},
     year = {2024},
     volume = {149},
     number = {4},
     doi = {10.21136/MB.2024.0120-23},
     mrnumber = {4840086},
     zbl = {07980807},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0120-23/}
}
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
SP  - 585
EP  - 602
VL  - 149
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0120-23/
DO  - 10.21136/MB.2024.0120-23
LA  - en
ID  - 10_21136_MB_2024_0120_23
ER  - 
%0 Journal Article
%A Niazian, Sogol
%A Aaly Kologani, Mona
%A Borzooei, Rajab Ali
%T Relative co-annihilators in lattice equality algebras
%J Mathematica Bohemica
%D 2024
%P 585-602
%V 149
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0120-23/
%R 10.21136/MB.2024.0120-23
%G en
%F 10_21136_MB_2024_0120_23
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

[1] Abujabal, H. A. S., Obaid, M. A., Aslam, M., Thaheem, A. B.: On annihilators of BCK-algebras. Czech. Math. J. 45 (1995), 727-735. | DOI | MR | JFM

[2] Borzooei, R. A., Zebardast, F., Kologani, M. Aaly: Some type filters in equality algebras. Categ. Gen. Algebr. Struct. Appl. 7 (2017), 33-55. | MR | JFM

[3] Burris, S., Sankappanavar, H. P.: A Course in Universal Algebra. Graduate Texts in Mathematics 78. Springer, New York (1981). | DOI | MR | JFM

[4] Ciungu, L. C.: Internal states on equality algebras. Soft Comput. 19 (2015), 939-953. | DOI | JFM

[5] Davey, B. A.: Some annihilator conditions on distributive lattices. Algebra Univers. 4 (1974), 316-322. | DOI | MR | JFM

[6] Filipoiu, A.: About Baer extensions of MV-algebras. Math. Jap. 40 (1994), 235-241. | MR | JFM

[7] Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic-Studia Logica Library 4. Kluwer Academic, Dordrecht (1998). | DOI | MR | JFM

[8] Halaš, R.: Annihilators in BCK-algebras. Czech. Math. J. 53 (2003), 1001-1007. | DOI | MR | JFM

[9] Jenei, S.: Equality algebras. Stud. Log. 100 (2012), 1201-1209. | DOI | MR | JFM

[10] Jenei, S., Kóródi, L.: On the variety of equality algebras. Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology Atlantis Press, Amsterdam (2011), 153-155. | DOI | JFM

[11] Leuştean, L.: Some algebraic properties of non-commutative fuzzy structures. Stud. Inf. Control 9 (2000), 365-370.

[12] Leuştean, L.: Baer extensions of BL-algebras. J. Mult.-Val. Log. Soft Comput. 12 (2006), 321-336. | MR | JFM

[13] Maroof, F. G., Saeid, A. Borumand, Eslami, E.: On co-annihilators in residuated lattices. J. Intell. Fuzzy Syst. 31 (2016), 1263-1270. | DOI | MR | JFM

[14] Meng, B. L., Xin, X. L.: Generalized co-annihilator of BL-algebras. Open Math. 13 (2015), 639-654. | DOI | MR | JFM

[15] Niazian, S., Kologani, M. Aaly, Arya, S. Homayon, Borzooei, R. A.: On co-annihilators in equality algebras. Miskolc Math. Notes 24 (2023), 933-951. | DOI | MR | JFM

[16] Paad, A.: Ideals in bounded equality algebras. Filomat 33 (2019), 2113-2123. | DOI | MR | JFM

[17] Turunen, E.: BL-algebras of basic fuzzy logic. Mathware Soft Comput. 6 (1999), 49-61. | MR | JFM

[18] Xu, Y., Ruan, D., Qin, K., Liu, J.: Lattice-Valued Logic: An Alternative Approach to Treat Fuzziness and Incomparability. Studies in Fuzziness and Soft Computing 132. Springer, Berlin (2003). | DOI | MR | JFM

[19] Zebardast, F., Borzooei, R. A., Kologani, M. Aaly: Results on equality algebras. Inf. Sci. 381 (2017), 270-282. | DOI | MR | JFM

[20] Zou, Y. X., Xin, X. L., He, P. F.: On annihilators in BL-algebras. Open Math. 14 (2016), 324-337. | DOI | MR | JFM

Cité par Sources :