Discriminator varieties of Boolean algebras with residuated operators

• Autorzy: Peter Jipsen
• Języki publikacji: EN

Abstrakty

EN

The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated monoids are discriminator algebras, provided they are subdirectly irreducible. These results are then used to give equational bases for some varieties of r-algebras. We also show that the variety of all residuated Boolean monoids is not a discriminator variety, which answers a question of B. Jónsson.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1993
• Tom: 28
• Numer: 1
• Strony: 239-252

Daty

wydano

1993

Twórcy

autor

Peter Jipsen

• Department of Mathematics, Iowa State University, 400 Carver Hall, Ames, Iowa 50011, U.S.A.

Bibliografia

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