Perfect extensions of de Morgan algebras

Haviar, Miroslav, 1965- Perfect extensions of de Morgan algebras / Miroslav Haviar, Miroslav Ploščica. -- An algebra A is called a perfect extension of its subalgebra B if every congruence of B has a unique extension to A. This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that A is a congruence-preserving extension of B. Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra M is perfect extension of its Boolean subalgebra B(M), the so-called skeleton of M. In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution.

In Algebra Universalis. -- Basel : Springer Nature Switzerland AG, 2021. -- ISSN 0002-5240. -- ISSN 1420-8911. -- Vol. 82, no. 4 (2021), art. no. 58, pp. 1-8

1. De Morganova algebra 2. MS-algebra 3. rozšírenie 4. Boolean algebra 5. články

I. Ploščica, Miroslav
II. Algebra Universalis. -- Vol. 82, no. 4 (2021), art. no. 58, pp. 1-8
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