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Are basic algebras residuated structures?
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DOI：10.1007/s00500-009-0399-z.png)
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MV-algebras are bounded commutative integral residuated lattices satisfying the double negation and the divisibility laws. Basic algebras were introduced as a certain generalization of MV-algebras (where associativity and commutativity of the binary operation is neglected). Hence, there is a natural question if also basic algebras can be considered as residuated lattices. We prove that for commutative basic algebras it is the case and for non-commutative ones we involve a modified adjointness condition which gives rise a new generalization of a residuated lattice.
Keyword:
Basic algebra
Commutative basic algebra
Residuated lattice
Residuated groupoid
Skew adjointness property
期刊
IF:
2.5
论文数:
1.0W
被引数:
2.1W
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