Finite Projective Distributive Lattices
1970 ◽
Vol 13
(1)
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pp. 139-140
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Keyword(s):
The theorem stated below is due to R. Balbes. The present proof is direct; it uses only the following two well-known facts: (i) Let K be a category of algebras, and let free algebras exist in K; then an algebra is projective if and only if it is a retract of a free algebra, (ii) Let F be a free distributive lattice with basis {xi | i ∊ I}; then ∧(xi | i ∊ J0) ≤ ∨(xi | i ∊ J1) implies J0∩J1≠ϕ. Note that (ii) implies (iii): If for J0 ⊆ I, a, b ∊ F, ∧(xi | i ∊ J0)≤a ∨ b, then ∧ (xi | i ∊ J0)≤ a or b.
Keyword(s):
2021 ◽
Vol 14
(3)
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pp. 207-217
1971 ◽
Vol 23
(5)
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pp. 866-874
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1975 ◽
Vol 19
(2)
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pp. 238-246
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Keyword(s):
1972 ◽
Vol 7
(3)
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pp. 377-385
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2015 ◽
Vol 08
(03)
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pp. 1550039
1981 ◽
Vol 24
(2)
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pp. 161-203
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