Displaying similar documents to “Modularity and distributivity of the lattice of Σ -closed subsets of an algebraic structure”

Σ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

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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 ( j , k ) -symmetrical functions

Piotr Liczberski, Jerzy Połubiński (1995)

Mathematica Bohemica

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n the present paper the authors study some families of functions from a complex linear space X into a complex linear space Y . They introduce the notion of ( j , k ) -symmetrical function ( k = 2 , 3 , ⋯ ; j = 0 , 1 , ⋯ , k - 1 ) which is a generalization of the notions of even, odd and k -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset U of X can be uniquely represented as the sum of an even function and an odd function.