Generalized co-annihilator of BL-algebras
Biao Long Meng ; Xiao Long Xin
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x-1F where F is a filter, and study basic properties of generalized co-annihilators. We also introduce the notion of involutory filters relative to a filter F and prove that the set of all involutory filters relative to a filter with respect to the suit operations is a complete Boolean lattice and BL-algebra. We use the technology of generalized co-annihilators to give characterizations of prime filters and minimal prime filters, respectively. In particular, we give a representation of co-annihilators in the quotient algebra of a BL-algebra L via a filter F by means of generalized co-annihilators relative to F in L:

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:275972
@article{bwmeta1.element.doi-10_1515_math-2015-0060,
     author = {Biao Long Meng and Xiao Long Xin},
     title = {Generalized co-annihilator of BL-algebras},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0060}
}
Biao Long Meng; Xiao Long Xin. Generalized co-annihilator of BL-algebras. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0060/

[1] Cignoli R., Esteva F., Godo L., Torrens A., Basic Fuzzy Logic is the Logic of Continuous T -norm and Their Residua, Soft Comput., 2000, 12, 106-112. [Crossref]

[2] Dvure´censkij A., State on PseudoMV -algebras, Stud Log., 2001a , 68, 301-327.

[3] Dvure´censkij A., On PseudoMV -algebras, Soft Comput., 2001b, 5, 347-354. [Crossref]

[4] Dvure´censkij A., Every liner Pseudo BL-algebra admits a state, Soft Comput., 2007, 11, 347-354. [WoS]

[5] Flonder P., Georgescu G., Iorgulescu A., Psedo t-norms and Pseudo BL-algebras, Soft Comput., 2001, 5, 355-371. [WoS][Crossref] | Zbl 0995.03048

[6] Georgescu G., Iorgulescu A., Pseudo BL-algebras, Mult Valued Log., 2001, 6, 95-135.

[7] Georgescu G., Leustean L., Some class of Pseudo BL-algebras, J. Aust Math Soc., 2002, 73, 127-153. [Crossref] | Zbl 1016.03069

[8] HKajek P., Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. | Zbl 0937.03030

[9] Haveshki M., Saeid A B., Eslami E., Some types of filters in BL-algebras, Soft Computing, 2006, 10, 657-664. [WoS][Crossref] | Zbl 1103.03062

[10] Iorgulescu A., Iséki algebras, Connection with BL-algebras, Soft Computing, 2004, 8, 449-463. [Crossref][WoS] | Zbl 1075.06009

[11] Nola A D., Georgescu G., Iorgulescu A., Boolean products of BL-algebras, J. Math Anal Appl, 2000, 251, 106-131. | Zbl 0966.03055

[12] Nola A D., Georgescu G., Iorgulescu A., Pseudo BL-algebras: Part I,II, Mult Valued Log., 2002, 8, 673-714, 715-750. | Zbl 1028.06007

[13] Nola A D., Leustean L., Compact representations of BL-algebras, Arch Math Log., 2003, 42, 737-761. [Crossref] | Zbl 1040.03048

[14] Kondo M., Dudek W A., Filter Theory in BL-algebras, Soft Comput., 2008, 12, 419-423. [WoS][Crossref] | Zbl 1165.03056

[15] Leu¸stean L., Representations of Many-valued Algebras Ph.D. Thesis, University of Bucharest, Faculty of Mathematics and Computer Science, Roumania, 2003.

[16] Saeid A B., Motamed S., Normal Filters in BL-Algebras, World Applied Sciences Journal (Special Issue for Applied Math), 2009, 7, 70-76.

[17] Saeid A B., Ahadpanah A., Torkzadeh L., Smarandache BL-Algebras, J. Applied Logic, 2010, 8, 253-261.

[18] Turunen E., Mathematics behind Fuzzy Logic, Advances in Soft Computing, Heidelberg: Physica-Verlag, 1999. | Zbl 0940.03029

[19] Turunen E., BL-algebras of Basic Fuzzy Logic, Mathware & Soft Comp., 1999, 6, 49-61. | Zbl 0962.03020

[20] Turunen E., Boolean Deductive Systems of BL-algebras, Arch Math Logic, 2001, 40, 467-473. [Crossref] | Zbl 1030.03048

[21] Turunen E., Sessa S., Local BL-algebras, Mult-Valued Logic, 2001, 6, 229-249. | Zbl 1049.03045

[22] Zhang X H., Jun Y B., Doh M I., On Fuzzy Filters and Fuzzy Ideals of BL-algebras, Fuzzy Systems & Math, 2006, 20, 8-20. | Zbl 1333.03264