On subuniverses of lattices and semilattices
Delbrin Ahmed · 2022
puter scientist, engineer and polymath.Von Neumann is generally regarded as the foremost mathematician of his time and is said to be the last representative of the great mathematicians (see [39]).He integrated pure and applied sciences.Notions like von Neumann algebra, prizes and https://njszt.hu/hu are named after him.His excellence also manifested itself in lattice theory, and his work substantially contributed to the fact that lattice theory eventually became a separate branch of mathematics.The founder of lattice theory and Universal Algebra, Garrett Birkhoff himself wrote in [9] that "'John von Neumann's brilliant mind blazed over lattice theory like a meteor, during a brief period centering around 1935-1937."' and "'One wonders what would have been the effect on lattice theory, if von Neumann's intense two-year preoccupation with lattice theory had continued for twenty years!"'Another milestone in the history of lattice theory was the year 1971, when the first journal devoted to lattices was founded.This journal called Algebra Universalis is still going strong.Well, it is also devoted to universal algebra not just lattice theory, but these two branches have a lot in common at the topical level and personal level.The founder, George Grätzer, is famous for producing results, papers and monographs on lattice theory; his 61-times coauthor, Elégius Tamás Schmidt also deserves a mention.Within a Ph.D. thesis, we cannot hope to give a reasonable survey of what transpired in lattice theory after the progress made by Birkhoff and John von Neumann.Instead of doing so, the reader is referred to the paper Rota [45], and to introductory sections of the monographs Grätzer [33] and Roman [44].In addition to the above-mentioned lattice theorist Grätzer (Hungarian-Canadian) and Schmidt (Hungarian), it is worth mentioning that Hungarian lattice theorists Gábor Szász, András Huhn, Gábor Czédli and Sándor Radeleczki have made substantial contributions and have had a huge impact on this branch of mathematics with their researches.In the rest of our introduction, we restrict our attention to those results that directly motivated our work and are closely connected to it.In recent years, intensive research has been carried out on finite lattices.