%0 Journal Article %1 ISI:000270883200007 %A Dvurecenskij, Anatolij %C 233 SPRING ST, NEW YORK, NY 10013 USA %D 2010 %I SPRINGER %J SOFT COMPUTING %K Unital_l-group n-Perfect_GMV-algebra Representation GMV-algebra Perfect_GMV-algebra Cyclic_element Free_product %N 3 %P 257-264 %R 10.1007/s00500-009-0400-x %T Cyclic elements and subalgebras of GMV-algebras %V 14 %X We study cyclic elements of order n of GMV-algebras. The existence of cyclic elements is equivalent to the condition that a given GMV-algebra contains a copy of the MV-algebra Gamma(Z, n). Using cyclic elements, we describe necessary conditions which guarantee the existence of a greatest subalgebra belonging to the variety generated by Gamma(Z, n). This is true, e. g. for representable GMV-algebras. Finally, we use cyclic elements to prove the existence of a free product in various varieties of GMV-algebras.

@article{ISI:000270883200007, abstract = {{We study cyclic elements of order n of GMV-algebras. The existence of cyclic elements is equivalent to the condition that a given GMV-algebra contains a copy of the MV-algebra Gamma(Z, n). Using cyclic elements, we describe necessary conditions which guarantee the existence of a greatest subalgebra belonging to the variety generated by Gamma(Z, n). This is true, e. g. for representable GMV-algebras. Finally, we use cyclic elements to prove the existence of a free product in various varieties of GMV-algebras.}}, added-at = {2013-02-02T14:40:36.000+0100}, address = {233 SPRING ST, NEW YORK, NY 10013 USA}, affiliation = {Dvurecenskij, A (Reprint Author), Slovak Acad Sci, Inst Math, Stefanikova 49, Bratislava 81473, Slovakia. Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia.}, author = {Dvurecenskij, Anatolij}, author-email = {dvurecen@mat.savba.sk}, bdsk-file-1 = {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}, bdsk-url-1 = {http://dx.doi.org/10.1007/s00500-009-0400-x%7D}, biburl = {https://www.bibsonomy.org/bibtex/275d028b7b377315aefbfa8424e9cc93d/ks-plugin-devel}, cited-references = {BLUDOV VV, 2005, ALGEBRA LOGIC, V44, P370. CHANG CC, 1958, T AM MATH SOC, V88, P467. DARNEL MR, 1995, THEORY LATTICE ORDER. DINOLA A, 2000, J ALGEBRA, V225, P667. DINOLA A, 2008, COMMUN ALGEBRA, V36, P1221, DOI 10.1080/00927870701862852. DVURECENSKIJ A, 2001, STUDIA LOGICA, V68, P301. DVURECENSKIJ A, 2002, J AUST MATH SOC 3, V72, P427. DVURECENSKIJ A, 2007, COMMUN ALGEBRA, V35, P3370, DOI 10.1080/00927870701410769. DVURECENSKIJ A, 2008, J ALGEBRA, V319, P4921, DOI 10.1016/j.jalgebra.2008.03.027. DVURECENSKIJ A, 2009, ALGEBRA UNI IN PRESS. DVURECENSKIJ A, 2009, COMMUN ALGE IN PRESS. GEORGESCU G, 2001, MULTIPLE VALUED LOGI, V6, P95. GLASS AMW, 1981, LONDON MATH SOC LECT, V55. JAKUBIK J, 2003, CZECH MATH J, V53, P1031. KOPYTOV VM, 1994, THEORY LATTICE ORDER. MUNDICI D, 1986, J FUNCT ANAL, V65, P15. MUNDICI D, 1988, J ALGEBRA, V113, P89. RACHUNEK J, 2002, CZECH MATH J, V52, P255. TORRENS A, 1994, MATH LOGIC QUART, V40, P431.}, date-added = {2010-06-30 09:38:41 +0200}, date-modified = {2010-06-30 09:42:51 +0200}, doc-delivery-number = {507VL}, doi = {10.1007/s00500-009-0400-x}, file = {:Duvrečenskij/Cyclic elements and subalgebras of GMV-algebras.pdf:PDF}, funding-acknowledgement = {Center of Excellence SAS-Physics of Information ; VEGA {[}2/6088/26 SAV,]; Science and Technology Assistance Agency Bratislava, Slovakia {[}APVV-0071-06]; {[}I/2/2005]}, funding-text = {The author is indebted to the referee for his very careful reading and suggestions. The paper has been supported by the Center of Excellence SAS-Physics of Information-I/2/2005, the grant VEGA No. 2/6088/26 SAV, by Science and Technology Assistance Agency under the contract APVV-0071-06, Bratislava, Slovakia.}, groups = {public}, interhash = {ab6f8ec932c72f00bb6f9de3a332278d}, intrahash = {75d028b7b377315aefbfa8424e9cc93d}, issn = {1432-7643}, journal = {SOFT COMPUTING}, journal-iso = {{Soft Comput.}}, keywords = {Unital_l-group n-Perfect_GMV-algebra Representation GMV-algebra Perfect_GMV-algebra Cyclic_element Free_product}, keywords-plus = {{PSEUDO MV-ALGEBRAS; VARIETIES}}, language = {{English}}, month = {#FEB#}, number = 3, number-of-cited-references = {{19}}, pages = {257-264}, publisher = {{SPRINGER}}, subject-category = {{Computer Science, Artificial Intelligence; Computer Science, Interdisciplinary Applications}}, times-cited = {{0}}, timestamp = {2013-02-02T14:40:36.000+0100}, title = {Cyclic elements and subalgebras of GMV-algebras}, type = {{Article}}, unique-id = {{ISI:000270883200007}}, username = {keinstein}, volume = 14, year = 2010 }