-rings of characteristic two that are Boolean.
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Join-closed and meet-closed subsets in complete lattices
To every subset of a complete lattice we assign subsets , and define join-closed and meet-closed sets in . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.
Joins of congruences in -groups
Join-semilattices whose sections are residuated po-monoids
We generalize the concept of an integral residuated lattice to join-semilattices with an upper bound where every principal order-filter (section) is a residuated semilattice; such a structure is called a sectionally residuated semilattice. Natural examples come from propositional logic. For instance, implication algebras (also known as Tarski algebras), which are the algebraic models of the implication fragment of the classical logic, are sectionally residuated semilattices such that every section...
Join-semilattices with two-dimensional congruence amalgamation
We say that a ⟨∨,0⟩-semilattice S is conditionally co-Brouwerian if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e. x ≤ y for all ⟨x,y⟩ ∈ X × Y), there exists z ∈ S such that X ≤ z ≤ Y, and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X, Y, and Z of less than κ elements, for an infinite cardinal κ, we obtain the definition of a conditionally κ-co-Brouwerian...
Jordan-Hahn decomposition of signed weights on Finite orthogonality spaces.
Jordan-Hölder Theorem for Lines
J-subspace lattices and subspace M-bases
The class of J-lattices was defined in the second author’s thesis. A subspace lattice on a Banach space X which is also a J-lattice is called a J- subspace lattice, abbreviated JSL. Every atomic Boolean subspace lattice, abbreviated ABSL, is a JSL. Any commutative JSL on Hilbert space, as well as any JSL on finite-dimensional space, is an ABSL. For any JSL ℒ both LatAlg ℒ and (on reflexive space) are JSL’s. Those families of subspaces which arise as the set of atoms of some JSL on X are characterised...