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IMI/Publicaţii/CSJM/Ediţii/CSJM v.26, n.3 (78), 2018/

Imbrication algebras - algebraic structures of nesting order

Authors: Drugus Ioachim, Volodymyr G. Skobelev
Keywords: cancellative magma, Catalan number, Merkle tree, ordered pair, quasi-variety.

Abstract

This paper is about "imbrication algebras", universal algebras with one binary operator in their signature, the operator for formation of ordered pairs, called here "pairing operator", and with the "characteristic property of ordered pairs" as their sole axiom. These algebras have been earlier introduced by the first author as reducts of "aggregate algebras", universal algebras proposed as models for a set theory convenient for formalization of data structures. The term "aggregate" is used to generalize three fundamental notions of set theory: set, atom and ordered pair. Thus, this paper initiates the research of aggregate algebras by narrowing the focus to one type of their main reducts - the reduct which deals with ordered pairs.

Ioachim M. Drugus
Institute of Mathematics and Computer Science
5 Academiei str., MD-2028, Chisinau, Republic of Moldova
Phone: +373 699 79 938
E-mail:

Volodymyr G. Skobelev
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
40 Glushkova ave., Kyiv, Ukraine, 03187
Phone: +38 063 431 86 05
E-mail:

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