Kites and residuated lattices
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We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade kite, therefore, we call this algebra simply a kite. We describe subdirectly irreducible kites and we classify them. We show that the variety of integral residuated lattices generated by kites is generated by all finite-dimensional kites. In particular, we describe some homomorphisms among kites.
KeywordsResiduated lattice Kite algebra Subdirect irreducible kite Classification of kites
Mathematics Subject Classification03G10 03B50
The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped us to improve the presentation of the paper.