A structure theory for ordered sets

DOI10.1016/0012-365X(81)90201-6zbMath0459.06002MaRDI QIDQ1151913

Ivan Rival, Dwight Duffus

Publication date: 1981

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

direct productsretractsprime intervalsirreducible ordered setsorder varieties

Mathematics Subject Classification ID

Partial orders, general (06A06) Structure theory of lattices (06B05)

Related Items

Dismantlable graphs and posets, fixed clique property, Generalized varieties, Classes closed under isomorphisms, retractions, and products, Holes in ordered sets, Cores and retracts, Algebraic properties and dismantlability of finite posets, Relative polars in ordered sets, Fixed points of products and the strong fixed point property, From finite posets to chain complete posets having no infinite antichain, Reducible classes of finite lattices, Monotone clones, residual smallness and congruence distributivity, \(\kappa\)-embeddings of ordered sets, Descending chains and antichains of the unary, linear, and monotone subfunction relations, Is there a diagram invariant?, Generalizations of Tarski's fixed point theorem for order varieties of complete meet semilattices, Fixed point structures on a set-mapping pair and Cartesian product, Sets with structure, mappings and fixed point property: fixed point structures, Algebraic properties of crowns and fences, Diagrams, orientations, and varieties, NU Polymorphisms on Reflexive Digraphs, Retracts of abelian lattice ordered groups, Injective envelopes of transition systems and Ferrers languages, The cylinder of a relation and generalized versions of the nerve theorem, The retracts of Hamming graphs, Order varieties generated by finite posets, Posets Dismantlable by Doubly Irreducibles, Retractions onto series-parallel posets, Injective envelope and parallel decomposition of a transition system, Absolute retracts and varieties generated by chordal graphs, Powers of ordered sets, Varieties of posets, On homotopy types of Alexandroff spaces, On the extension of vertex maps to graph homomorphisms, All retraction operators on a complete lattice form a complete lattice, Dr-irreducibility of connected monounary algebras with a cycle, DR-irreducibility of connected monounary algebras, Strong Retracts of Unary Algebras, On a representation of monounary algebras, Representation of Connected Monounary Algebras by Means of Irreducibles, Partial order embeddings with convex range, Lattice of retracts of monounary algebras, Unnamed Item, Complete retract mappings of a complete lattice ordered group, Unnamed Item, A fixed point theorem for commuting families of relational homomorphisms. Applications to metric spaces, ordered sets and oriented graphs, Some complexity bounds for subtype inequalities, Order varieties generated by \(\vee\)-semilattices of finite width, Obituary: Ivan Rival, Algorithms for the fixed point property, Retract varieties of monounary algebras, Unnamed Item, The smallest graph variety containing all paths, Monotone Jónsson operations and near unanimity functions, Injective envelope of graphs and transition systems, An application of the Helly property to the partially ordered sets, Unnamed Item, A note on axiomatizable order varieties, The strong selection property and ordered sets of finite length, Every countable lattice is a retract of a direct product of chains, Isotone relations and the fixed point property for posets, Retract varieties of lattice ordered groups, Monotone clones and the varieties they determine, Antiatomic retract varieties of monounary algebras, Retract irreducibility of monounary algebras, Ordonnés escamotables et points fixes. (Dismantlable orders and fixed points)

Cites Work

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• Locally triangular graphs and normal quotients of the \(n\)-cube
• Spanning retracts of a partially ordered set
• The smallest order variety containing all chains
• Certain partially ordered sets of dimension three
• Characterization problems for graphs, partially ordered sets, lattices, and families of sets
• A fixed point theorem for finite partially orderes sets
• Path length in the covering graph of a lattice
• A decomposition theorem for partially ordered sets
• A lattice-theoretical fixpoint theorem and its applications
• A characterization of complete lattices
• Crowns, Fences, and Dismantlable Lattices
• Graphs Orientable as Distributive Lattices
• Fixed-edge theorem for graphs with loops
• Retracts and the Fixed Point Problem for Finite Partially Ordered Sets
• An Effective Version of Dilworth's Theorem
• Some Monotonicity Properties of Partial Orders
• A Logarithmic Property for Exponents of Partially Ordered Sets
• The FKG Inequality and Some Monotonicity Properties of Partial Orders
• Lattices with Doubly Irreducible Elements
• Planar Lattices
• Unoriented graphs of modular lattices
• Subdirect representations in axiomatic classes
• The 3-Irreducible Partially Ordered Sets
• Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints
• Undirected Graphs Realizable as Graphs of Modular Lattices
• A Characterization of Comparability Graphs and of Interval Graphs
• Partially Ordered Sets
• Partially Ordered Sets
• On the Construction of Partially Ordered Systems with a Given Group of Automorphisms
• The structure of Sperner k-families