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Keywords:
$\star$-autonomous lattice; pseudo $\star$-autonomous lattice; residuated lattice; ideal; normal ideal; congruence
$\star$-autonomous lattice; pseudo $\star$-autonomous lattice; residuated lattice; ideal; normal ideal; congruence
Summary:
Pseudo $\star $-autonomous lattices are non-commutative generalizations of $\star $-autonomous lattices. It is proved that the class of pseudo $\star $-autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo $\star $-autonomous lattices can be described as their normal ideals.
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