Are basic algebras residuated structures?

作者：Botur Michal^*; Chajda Ivan; Halas Radomir

来源：Soft Computing, 2010, 14(3): 251-255.

DOI：10.1007/s00500-009-0399-z

• Basic algebra
• Commutative basic algebra
• Residuated lattice
• Residuated groupoid
• Skew adjointness property

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.

• 出版日期2010-2