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Posets, homomorphisms and homogeneity Abstract
"... Jarik Neˇsetˇril suggested to the first author the investigation of notions of homogeneity for relational structures, where “isomorphism ” is replaced by “homomorphism” in the definition. Here we look in detail at what happens for posets. For the strict order, all five generalisations of homogeneity ..."
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of homogeneity coincide, and we give a characterisation of the countable structures that arise. For the nonstrict order, there is an additional class. The “generic poset ” plays an important role in the investigation. Key words: Poset, homomorphism, homogeneous, relational structure 1
The regular algebra of a poset
 Trans. Amer. Math. Soc
"... Abstract. Let K be a fixed field. We attach to each finite poset P a von Neumann regular Kalgebra QK(P) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective QK(P)modules is the abelian monoid generated by P with the only relations given by p = p + q ..."
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Cited by 6 (4 self)
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Abstract. Let K be a fixed field. We attach to each finite poset P a von Neumann regular Kalgebra QK(P) in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective QK(P)modules is the abelian monoid generated by P with the only relations given by p = p + q
Finiteness Theorems for Graphs and Posets Obtained by Compositions
 Order
, 1998
"... We investigate classes of graphs and posets that admit decompositions to obtain or disprove finiteness results for obstruction sets. To do so we develop a theory of minimal infinite antichains that allows us to characterize such antichains by means of the set of elements below it. In particular we ..."
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Cited by 3 (0 self)
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We investigate classes of graphs and posets that admit decompositions to obtain or disprove finiteness results for obstruction sets. To do so we develop a theory of minimal infinite antichains that allows us to characterize such antichains by means of the set of elements below it. In particular we
YosidaHewitt and Lebesgue decompositions of states on orthomodular posets
, 1997
"... Orthomodular posets are usually used as event structures of quantum mechanical systems. The states of the systems are described by probability measures (also called states) on it. It is well known that the family of all states on an orthomodular poset is a convex set, compact with respect to the pro ..."
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Cited by 2 (1 self)
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Hewitt decompositions as special cases. Considering, in particular, the problem of existence and uniqueness of such decompositions, we generalize to this setting numerous results obtained earlier only for orthomodular lattices and orthocomplete orthomodular posets. AMS class. 06C15, 81P10, 28A33. Key words
RECONSTRUCTION OF PATH ALGEBRAS FROM THEIR POSETS OF TILTING MODULES
"... Abstract. Let Λ = k − → ∆ be the path algebra of a finite quiver without oriented cycles. The set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set. We will show here that TΛ uniquely determines − → ∆if − → ∆ has no multiple arrows and no isola ..."
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Cited by 5 (0 self)
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Abstract. Let Λ = k − → ∆ be the path algebra of a finite quiver without oriented cycles. The set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set. We will show here that TΛ uniquely determines − → ∆if − → ∆ has no multiple arrows and no isolated vertices. Let Λ be a basic, connected finite dimensional algebra over an algebraically closed field k and let mod Λ be the category of finitely generated left Λmodules. For a module M ∈ mod Λ we denote by pd ΛM the projective dimension of M and by gl.dim Λ the global dimension of Λ. A module T ∈ mod Λ is called a tilting module if the following three conditions are satisfied: (i) pd ΛT<∞, (ii) Ext i Λ(T,T)=0for all i>0 and (iii) there exists an exact sequence 0 → ΛΛ → T 0 →···→T r → 0with T i ∈ add T for all 0 ≤ i ≤ r, where add T is the full subcategory of mod Λ whose objects are direct sums of direct summands of T. We will say that a tilting module is basic or multiplicity free if in a direct sum decomposition of T the indecomposable direct summands of T occur with multiplicity one. Unless stated otherwise all tilting modules considered here will be assumed to be basic.
1Quasihereditary algebras
"... Pučinskaitė Motivated by the structure of the algebras associated to the blocks of the BernsteinGelfandGelfandcategory O, we define a subclass of quasihereditary algebras called 1quasihereditary. Many properties of these algebras only depend on the defining partial order. In particular, we ca ..."
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Pučinskaitė Motivated by the structure of the algebras associated to the blocks of the BernsteinGelfandGelfandcategory O, we define a subclass of quasihereditary algebras called 1quasihereditary. Many properties of these algebras only depend on the defining partial order. In particular, we
Results 1  10
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588