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Lattices of annihilators in commutative algebras over fields

Jastrzębska M., Krempa J.

Demonstratio Mathematica

2015

Vol. 48, nr 4

546--553

Let K be any field and L be any lattice. In this note we show that L is a sublattice of annihilators in an associative and commutative K-algebra. If L is finite, then our algebra will be finite dimensional over K.

Standard QBCC-algebras

Halaš R., Ort J.

Demonstratio Mathematica

2003

Vol. 36, nr 1

1--10

The class of QBBC-algebras was introduced and studied by the authors in ioj. These algebras model properties of the logical connective implication "=>" in which tin- validity of formulas x => y and y => x does not imply the equivalence of x and y. In ihe paper the properties of standard QBCC-algebras derived from qosets are studied.

Order algebras

Chajda I., Halaš R.

Demonstratio Mathematica

2002

Vol. 35, nr 1

1-10

To every ordered set with a greatest element is assigned an order algebra, a Hilbert algebra occuring in intuicionistic logic. We prove some basic properties of order algebras and characterize their ideals and congruences. We introduce a concept of (relative) annihilator and show that it is a (relative) pseudocomplement in the lattice of all ideals.