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2 Demonstratio Mathematica

2 2011

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Representation of modals

Pilitowska A., Zamojska-Dzienio A.

Demonstratio Mathematica

2011

Vol. 44, nr 3

535-556

The main aim of this paper is to describe the free objects in arbitrary varieties of modals (semilattice ordered idempotent and entropic algebras)and give some new representations of modals.

Embedding sums of cancellative modes into functorial sums

Romanowska A. B., Stronkowski M., Zamojska-Dzienio A.

Demonstratio Mathematica

2011

Vol. 44, nr 3

557-569

The paper discusses a representation of modes (idempotent and entropic algebras)as subalgebras of so called functorial sums of cancellative algebras.We show that each mode that has a homomorphism onto an algebra satisfying a certain additional condition,with corresponding cancellative congruence classes,embeds into a functorial sum of cancellative algebras.We also discuss typical applications of this result.