Note on distributive posets
نویسندگان
چکیده
منابع مشابه
Characterizations of 0-distributive Posets
The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
متن کاملPosets That Locally Resemble Distributive Lattices
Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a ...
متن کاملA Note on Blockers in Posets
The blocker A∗ of an antichain A in a finite poset P is the set of elements minimal with the property of having with each member of A a common predecessor. The following is done: (1) The posets P for which A∗∗ = A for all antichains are characterized. (2) The blocker A∗ of a symmetric antichain in the partition lattice is characterized. (3) Connections with the question of finding minimal size ...
متن کاملA note on infinitely distributive inverse semigroups
By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...
متن کاملDistributive Substructural Logics as Coalgebraic Logics over Posets
We show how to understand frame semantics of distributive substructural logics coalgebraically, thus opening a possibility to study them as coalgebraic logics. As an application of this approach we prove a general version of Goldblatt-Thomason theorem that characterizes definability of classes of frames for logics extending the distributive Full Lambek logic, as e.g. relevance logics, many-valu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICS FOR APPLICATIONS
سال: 2012
ISSN: 1805-3610,1805-3629
DOI: 10.13164/ma.2012.13