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Generalized BL-algebras

Abbreviation: GBL

Definition

A \emph{generalized BL-algebra} is a residuated lattice L=L,,,,e,,/ such that

xy=y(yxe), xy=(x/ye)y

Morphisms

Let L and M be generalized BL-algebras. A morphism from L to M is a function h:LM that is a homomorphism:

h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(xy)=h(x)h(y), h(x/y)=h(x)/h(y), h(e)=e

Examples

Example 1:

Basic results

Properties

Finite members

n 1 2 3 4 5 6 7 8 9 10 11
# of algs 1 1 2 5 10 23 49 111
# of si's 1 1 2 4 9 19 42 97

Subclasses

Superclasses

References


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