FREE TERNARY ALGEBRAS
2000 ◽
Vol 10
(06)
◽
pp. 739-749
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Keyword(s):
A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L. With this characterization, the free ternary algebra on one free generator is displayed. The poset of join irreducibles of finitely generated free ternary algebras is characterized. The uniqueness of the set of free generators and their pseudocomplements is also established.
2001 ◽
Vol 26
(9)
◽
pp. 539-545
1979 ◽
Vol 28
(3)
◽
pp. 335-345
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1971 ◽
Vol 12
(2)
◽
pp. 187-192
1988 ◽
Vol 31
(3)
◽
pp. 374-379
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2018 ◽
Vol 17
(02)
◽
pp. 1850023
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2004 ◽
Vol 03
(02)
◽
pp. 207-217
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1981 ◽
Vol 1
(2)
◽
pp. 209-221
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2014 ◽
Vol 13
(08)
◽
pp. 1450060
2016 ◽
Vol 15
(08)
◽
pp. 1650145
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