Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
13.05.1939
E-mail: Keywords: universal algebra; lattices; varieties of semigroups; automata; graphs.
Subject:
An abstract characterization of semigroups of partial transformations considered together with the inclusion relations of their first and second projections and the semiconsistensy relation was obtained (1968). It is shown that any complete uniquely complemented lattice is isomorphic to a direct product of a complete atomic Boolean algebra and a complete atomless uniquely complemented lattice (1982). It is proved that any complete lattice is isomorphic to the lattice of all subsets of some set that are closed under a suitable elementary closure operation (i.e. when every closed subset is the closure of some point) (1984). Quasi-boolean lattices and associations were defined and it was established that associations were exactly groupoids of full one-to-one quasi-boolean transformations of sets (1986). In a number of papers published in 1990-2001 groupoids were described which can be embedded in quasi-boolean powers of semigroups from minimal semigroup varieties. Two monographs were devoted to algebra of discrete systems (1988, 1997).
Main publications:
Salii V. N., Reshetki s edinstvennymi dopolneniyami, Nauka, M., 1984 ; perevod: Salii V. N., Lattices with unique complements, Amer. Math. Soc., Providence, RI, 1988
Salii V. N., “Quasi-Boolean lattices and associations”, Lectures in universal algebra (Szeged, 1983), Colloq. Math. Soc. János Bolyai, 43, North-Holland, Amsterdam, 1986, 429–454
Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 1997
Salii V. N., “Kvazibulevy stepeni polureshetok”, Izv.vuzov. Matematika, 1999, № 7, 54–60
; perevod: Salii V. N., Lattices with unique complements, Amer. Math. Soc., Providence, RI, 1988 
