On maximal ideals of pseudo-BCK-algebras
Andrzej Walendziak
Discussiones Mathematicae - General Algebra and Applications, Tome 31 (2011), p. 61-73 / Harvested from The Polish Digital Mathematics Library

We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:276652
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     title = {On maximal ideals of pseudo-BCK-algebras},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {31},
     year = {2011},
     pages = {61-73},
     zbl = {1261.06024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1175}
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Andrzej Walendziak. On maximal ideals of pseudo-BCK-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 31 (2011) pp. 61-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1175/

[000] [1] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. doi: 10.1090/S0002-9947-1958-0094302-9 | Zbl 0084.00704

[001] [2] G. Dymek and A. Walendziak, On maximal ideals of pseudo MV-algebras, Commentationes Mathematicae 42 (2007), 117-126.

[002] [3] G. Dymek and A. Walendziak, Fuzzy ideals of pseudo-BCK-algebras, submitted.

[003] [4] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Dordrecht-Boston-London 2000.

[004] [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, p. 961-968 in: 'The Proc. of the Fourth International Symp. on Economic Informatics', Bucharest, Romania 1999. | Zbl 0985.06007

[005] [6] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, p. 90-92 in: 'Abstracts of the Fifth International Conference FSTA 2000', Slovakia 2000.

[006] [7] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, p. 97-114 in: 'Proc. of DMTCS'01: Combinatorics, Computability and Logic', Springer, London 2001. doi: 10.1007/978-1-4471-0717-0_9 | Zbl 0986.06018

[007] [8] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras, Multiplae-Valued Logic 6 (2001), 95-135. | Zbl 1014.06008

[008] [9] P. Hájek, Metamathematics of fuzzy logic, Inst. of Comp. Science, Academy of Science of Czech Rep., Technical report 682 (1996). | Zbl 0937.03030

[009] [10] P. Hájek, Metamathematics of fuzzy logic, Kluwer Acad. Publ., Dordrecht, 1998. | Zbl 0937.03030

[010] [11] R. Halaš and J. Kühr, Deductive systems and annihilators of pseudo-BCK algebras, Ital. J. Pure Appl. Math., submitted. | Zbl 1184.06011

[011] [12] Y. Imai and K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22. doi: 10.3792/pja/1195522169 | Zbl 0156.24812

[012] [13] A. Iorgulescu, Classes of pseudo-BCK algebras, Part I, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 71-130. | Zbl 1147.06011

[013] [14] A. Iorgulescu, Classes of pseudo-BCK algebras, Part II, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 575-629. | Zbl 1154.06011

[014] [15] A. Iorgulescu, Algebras of logic as BCK algebras, submitted.

[015] [16] K. Isěki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japonicae 21 (1976), 351-366. | Zbl 0355.02041

[016] [17] Y.B. Jun, Characterizations of pseudo-BCK algebras, Scientiae Mathematicae Japonicae 57 (2003), 265-270. | Zbl 1021.06504

[017] [18] J. Kühr, Pseudo-BCK-algebras and related structures, Univerzita Palackého v Olomouci 2007. | Zbl 1140.06008

[018] [19] J. Kühr, Representable pseudo-BCK-algebras and integral residuated lattices, Journal of Algebra 317 (2007), 354-364. doi: 10.1016/j.jalgebra.2007.07.003 | Zbl 1140.06008

[019] [20] J. Rachůnek, A non-commutative generalization of MV algebras, Czechoslovak Math. J. 52 (2002), 255-273. | Zbl 1012.06012