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On the definition and the representability of quasi‐polyadic equality algebras
Author(s) -
Ferenczi Miklós
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201100109
Subject(s) - mathematics , commutative property , axiom , set (abstract data type) , pure mathematics , non associative algebra , nest algebra , interior algebra , algebra over a field , algebra representation , computer science , geometry , programming language
We show that the usual axiom system of quasi polyadic equality algebras is strongly redundant. Then, so called non‐commutative quasi‐polyadic equality algebras are introduced ( QPEN α ), in which, among others, the commutativity of cylindrifications is dropped. As is known, quasi‐polyadic equality algebras are not representable in the classical sense, but we prove that algebras in QPEN α are representable by quasi‐polyadic relativized set algebras, or more exactly by algebras in Gwq α .
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