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Σ -Hamiltonian and Σ -regular algebraic structures

Ivan Chajda, Petr Emanovský (1996)

Mathematica Bohemica

The concept of a -closed subset was introduced in [1] for an algebraic structure = ( A , F , R ) of type and a set of open formulas of the first order language L ( ) . The set C ( ) of all -closed subsets of forms a complete lattice whose properties were investigated in [1] and [2]. An algebraic structure is called - hamiltonian, if every non-empty -closed subset of is a class (block) of some congruence on ; is called - regular, if = 𝔽 for every two , 𝔽 ∈ whenever they have a congruence class B ∈ C ( ) in common....

Σ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

For an algebraic structure = ( A , F , R ) or type and a set Σ of open formulas of the first order language L ( ) we introduce the concept of Σ -closed subsets of . The set ℂ Σ ( ) of all Σ -closed subsets forms a complete lattice. Algebraic structures , of type are called Σ -isomorphic if ℂ Σ ( ) ≅ ℂ Σ ( ) . Examples of such Σ -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study Σ -isomorphic algebraic structures in dependence on the...

Currently displaying 221 – 240 of 250