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EXTERNALLY COMPATIBLE IDENTITIES OF ALGEBRAS

EXTERNALLY COMPATIBLE IDENTITIES OF ALGEBRAS DEMONSTRATIO MATHEMATICAvol xxniNo 2inoWiestawa ChromikEXTERNALLY COMPATIBLE IDENTITIES OF ALGEBRAS0 . Let r : T — - N U {o} be a type of algebras and [ f }mily of fundamental operation symbols, associated withteTi s a fa-r .If K i s a variety, of algebras of type r , we denote by E (K ) theset of all identities of type z satisfied in K .F o r a set E of identities of type r , we denote by V ( E ) the var i e t y of type r defined by E .In this paper we introduce a new type of identities, namely socalled externally compatible identities.If K i s an idempotent variety of algebras or a variety of B o o l e ' ana l g e b r a s , then we d e s c r i b e algebras from the v a r i e t y V ( E x ( K ) ) ,whereE x ( K ) i s the set of all externally compatible identities belonging toE ( K ) . We also construct equational base of V ( E x ( K ) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

EXTERNALLY COMPATIBLE IDENTITIES OF ALGEBRAS

Chromik, Wiestawa
Demonstratio Mathematica , Volume 23 (2): 12 – Apr 1, 1990
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Publisher
de Gruyter
Copyright
© by Wiestawa Chromik
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1990-0208
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAvol xxniNo 2inoWiestawa ChromikEXTERNALLY COMPATIBLE IDENTITIES OF ALGEBRAS0 . Let r : T — - N U {o} be a type of algebras and [ f }mily of fundamental operation symbols, associated withteTi s a fa-r .If K i s a variety, of algebras of type r , we denote by E (K ) theset of all identities of type z satisfied in K .F o r a set E of identities of type r , we denote by V ( E ) the var i e t y of type r defined by E .In this paper we introduce a new type of identities, namely socalled externally compatible identities.If K i s an idempotent variety of algebras or a variety of B o o l e ' ana l g e b r a s , then we d e s c r i b e algebras from the v a r i e t y V ( E x ( K ) ) ,whereE x ( K ) i s the set of all externally compatible identities belonging toE ( K ) . We also construct equational base of V ( E x ( K )

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 1990

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