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Keywords:
equality algebra; annihilator; co-annihilator; relative co-annihilator; filter
equality algebra; annihilator; co-annihilator; relative co-annihilator; filter
Summary:
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.
References:
[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 10.1023/B:CMAJ.0000024536.04596.67 | MR 1354929 | Zbl 0847.06009
[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 3681517 | Zbl 1423.03257
[3] Burris, S., Sankappanavar, H. P.: A Course in Universal Algebra. Graduate Texts in Mathematics 78. Springer, New York (1981). DOI 10.1007/978-1-4613-8130-3 | MR 0648287 | Zbl 0478.08001
[4] Ciungu, L. C.: Internal states on equality algebras. Soft Comput. 19 (2015), 939-953. DOI 10.1007/s00500-014-1494-3 | Zbl 1392.06013
[5] Davey, B. A.: Some annihilator conditions on distributive lattices. Algebra Univers. 4 (1974), 316-322. DOI 10.1007/BF02485743 | MR 0357261 | Zbl 0299.06007
[6] Filipoiu, A.: About Baer extensions of MV-algebras. Math. Jap. 40 (1994), 235-241. MR 1297237 | Zbl 0808.06015
[7] Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic-Studia Logica Library 4. Kluwer Academic, Dordrecht (1998). DOI 10.1007/978-94-011-5300-3 | MR 1900263 | Zbl 0937.03030
[8] Halaš, R.: Annihilators in BCK-algebras. Czech. Math. J. 53 (2003), 1001-1007. DOI 10.1023/B:CMAJ.0000024536.04596.67 | MR 2018845 | Zbl 1080.06035
[9] Jenei, S.: Equality algebras. Stud. Log. 100 (2012), 1201-1209. DOI 10.1007/s11225-012-9457-0 | MR 3001053 | Zbl 1270.03138
[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 10.2991/eusflat.2011.1 | Zbl 1254.08004
[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 2288820 | Zbl 1165.03057
[13] Maroof, F. G., Saeid, A. Borumand, Eslami, E.: On co-annihilators in residuated lattices. J. Intell. Fuzzy Syst. 31 (2016), 1263-1270. DOI 10.3233/IFS-162192 | MR 3469089 | Zbl 1366.03241
[14] Meng, B. L., Xin, X. L.: Generalized co-annihilator of BL-algebras. Open Math. 13 (2015), 639-654. DOI 10.1515/math-2015-0060 | MR 3414771 | Zbl 1347.03109
[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 10.18514/MMN.2023.3816 | MR 4619775 | Zbl 7777173
[16] Paad, A.: Ideals in bounded equality algebras. Filomat 33 (2019), 2113-2123. DOI 10.2298/FIL1907113P | MR 4036366 | Zbl 1499.06072
[17] Turunen, E.: BL-algebras of basic fuzzy logic. Mathware Soft Comput. 6 (1999), 49-61. MR 1724318 | Zbl 0962.03020
[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 10.1007/978-3-540-44847-1 | MR 2027329 | Zbl 1048.03003
[19] Zebardast, F., Borzooei, R. A., Kologani, M. Aaly: Results on equality algebras. Inf. Sci. 381 (2017), 270-282. DOI 10.1016/j.ins.2016.11.027 | MR 3584860 | Zbl 1429.03219
[20] Zou, Y. X., Xin, X. L., He, P. F.: On annihilators in BL-algebras. Open Math. 14 (2016), 324-337. DOI 10.1515/math-2016-0029 | MR 3505725 | Zbl 1349.06034
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