2018/02/14 by Claudia Mureșan, Muresan, Claudia
Computer Science · Decision Sciences · #06F99 #08A30 #Advanced Algebra and Logic #FOS: Mathematics #Multi-Criteria Decision Making #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1802.05344
openalex publication_date 2018/02/14 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper, we characterize the congruences of an arbitrary i--lattice,\ninvestigate the structure of the lattice they form and how it relates to the\nstructure of the lattice of lattice congruences, then, for an arbitrary\nnon--zero natural number n, we determine the largest possible number of\ncongruences of an n--element i--lattice, along with the structures of the\nn--element i--lattices with this number of congruences. Our characterizations\nof the congruences of i--lattices have useful corollaries: determining the\ncongruences of i--chains, the congruence extension property of the variety of\ndistributive i--lattices, a description of the atoms of the congruence lattices\nof i--lattices, characterizations for the subdirect irreducibility of\ni--lattices. In terms of the relation between the above--mentioned problem on\nnumbers of congruences of finite i--lattices and its analogue for lattices,\nwhile the n--element i--lattices with the largest number of congruences turn\nout to be exactly the n--element lattices whose number of congruences is\neither the largest or the second largest possible, we provide examples of pairs\nof n--element i--lattices and even pseudo--Kleene algebras such that one of\nthem has strictly more congruences, but strictly less lattice congruences than\nthe other.\n