C. C. Chen, K. M. Koh and S. K. Tan, `Frattini sublattices of distributive lattices', Algebra Universalis, 3 (1973) 294--303.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The investigation of covering relations in SubL is, in essence, an investigation of maximal sublattices. One of the earliest contributions to the study of maximal sublattices of distributive lattices was made in 1952 by Hashimoto [11] During the 1970 s the work of Adams [2] Chen, Koh and Tan [8], and Rival [18, 19] carried these investigations forward. In recent years, Abad and Adams [1] Adams, Dwinger and Schmid [3] Ryter and Schmid [20] and Vogt [22] have added considerably to our understanding of maximal sublattices of finite distributive lattices. In addition, the recent paper of ....

....connection between L and Q(L) induced by the relation #, see also Vogt [22] Although the dual isomorphisms in Rival [19] and the one presented here have some elements in common, there does not seem to be a trivial transition from one to the other. 8 Zsolt Lengvarszky and George F. McNulty [8] 3. The Proof of Theorem 2: Coverings in Sub L Proof. Let L be a finite distributive lattice, let K # Sub L,andletx#L K with K # =Sg L (K# x ) There are four statements to prove: 1) If x =0 K # ,thenK # covers K and #(K # ) 1 #(K) 2) If x =1 K # ,thenK # covers K and #(K # ) 1 #(K) ....

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C. C. Chen, K. M. Koh and S. K. Tan, `Frattini sublattices of distributive lattices', Algebra Universalis, 3 (1973) 294--303.

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Chen, C. C., Koh, K. M., and Tan, S. K., Frattini sublattices of distributive lattices, Algebra Universalis 3 (1973), 294 -- 303

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