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The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Pavel Růžička (2017)

Commentationes Mathematicae Universitatis Carolinae

We attach to each 〈 0 , ∨ 〉 -semilattice S a graph G S whose vertices are join-irreducible elements of S and whose edges correspond to the reflexive dependency relation. We study properties of the graph G S both when S is a join-semilattice and when it is a lattice. We call a 〈 0 , ∨ 〉 -semilattice S particle provided that the set of its join-irreducible elements satisfies DCC and join-generates S . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...

The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . ℤ and ℝ denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 ⊆ W be non-void and not { { 0 } } . We show(1) H S P 𝒢 = H S P ( H S 𝒢 ∩ S ℝ ) , and(2) W ≠ 𝒢 = H S P 𝒢 if and only if ∃ V ( 𝒢 = H S P { 1 v ℤ | v ∈ V } ) . Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted...

The Joly–Becker theorem for * –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the * –version of the Joly–Becker theorem: a skew field admits a * –ordering of level n iff it admits a * –ordering of level n ℓ for some (resp. all) odd ℓ ∈ ℕ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a * –ordering of higher level also admits a * –ordering of level 1 . Every field that admits a * –ordering of higher level admits a * –ordering of level 1 or 2

The Kadison problem on a class of commutative Banach algebras with closed cone

M. A. Toumi (2010)

Commentationes Mathematicae Universitatis Carolinae

The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra A that all of its squares are positive and satisfying the following property: Every continuous bilinear map Φ from A × A into an arbitrary Banach space B such that Φ ( a , b ) = 0 whenever a b = 0 , satisfies the condition Φ ( a b , c ) = Φ ( a , b c ) for all a , b , c ∈ A .

Currently displaying 81 – 100 of 304