Clausal relations and {C}-clones | Zendy

Edith Mireya Vargas | Zendy

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Clausal relations and {C}-clones

Author(s) -

Edith Mireya Vargas

Publication year - 2010

Publication title -

discussiones mathematicae - general algebra and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.127

H-Index - 2

eISSN - 2084-0373

pISSN - 1509-9415

DOI - 10.7151/dmgaa.1167

Subject(s) - finitary , galois connection , mathematics , connection (principal bundle) , set (abstract data type) , complete boolean algebra , complete lattice , discrete mathematics , finite set , lattice (music) , infinite set , combinatorics , algebra over a field , pure mathematics , two element boolean algebra , computer science , mathematical analysis , physics , geometry , universality (dynamical systems) , quantum mechanics , acoustics , filtered algebra , programming language

We introduce a special set of relations called clausal relations. We study a Galois connection Pol−C Inv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol− Inv. We define C clones as the Galois closed sets of operations with respect to Pol−C Inv and describe the lattice of all C -clones for the Boolean caseD = {0, 1}. Finally we prove certain results about C -clones over a larger set.

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