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Salii, Viacheslav Nikolaevich
Statistics Math-Net.Ru
Total publications: 30
Scientific articles: 30

Number of views:
This page:3425
Abstract pages:6979
Full texts:2978
References:837
Professor
Candidate of physico-mathematical sciences (1965)
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).

Biography

Graduated from Faculty of Mathematics and Mechanics of Saratov State University in 1962 (Department of Geometry). Ph.D. thesis was defended in 1965. A list of my works contains more than 100 titles, including 4 monographs (in lattice theory and applied algebra). 14 Ph.D. theses were completed under my supervision.
   
Main publications:
  1. Salii V. N., Reshetki s edinstvennymi dopolneniyami, Nauka, M., 1984  mathscinet  zmath; perevod: Salii V. N., Lattices with unique complements, Amer. Math. Soc., Providence, RI, 1988  mathscinet  zmath
  2. 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  mathscinet
  3. Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 1997  mathscinet  zmath
  4. Salii V. N., “Kvazibulevy stepeni polureshetok”, Izv.vuzov. Matematika, 1999, № 7, 54–60  mathnet  mathscinet  zmath
  5. Salii V. N., “Kvazibulevy stepeni elementarnykh 2-grupp”, Matem. zametki, 69:6 (2001), 899–905  mathnet  mathscinet  zmath

https://www.mathnet.ru/eng/person17973
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/202354

Publications in Math-Net.Ru Citations
2016
1. V. N. Salii, “The Sperner property for polygonal graphs considered as partially ordered sets”, Izv. Saratov Univ. Math. Mech. Inform., 16:2 (2016),  226–231  mathnet  mathscinet  elib
2. V. N. Salii, “On the number of Sperner vertices in a tree”, Prikl. Diskr. Mat., 2016, no. 2(32),  115–118  mathnet
2015
3. V. N. Salii, “The Sperner property for trees”, Prikl. Diskr. Mat. Suppl., 2015, no. 8,  124–127  mathnet 2
2014
4. V. N. Salii, “The Sperner property for polygonal graphs”, Prikl. Diskr. Mat. Suppl., 2014, no. 7,  135–137  mathnet 2
2013
5. V. N. Salii, “The ordered set of connected parts of a polygonal graph”, Izv. Saratov Univ. Math. Mech. Inform., 13:2(2) (2013),  44–51  mathnet 4
6. V. N. Salii, “On the ordered set of connected parts of a polygonal graph”, Prikl. Diskr. Mat. Suppl., 2013, no. 6,  87–89  mathnet
2012
7. V. N. Salii, “The system of abstract connected subgraphs of a linear graph”, Prikl. Diskr. Mat., 2012, no. 2(16),  90–94  mathnet 2
2011
8. V. N. Salii, “On skeleton automata”, Prikl. Diskr. Mat., 2011, no. supplement № 4,  76–78  mathnet
9. V. N. Salii, “Skeleton automata”, Prikl. Diskr. Mat., 2011, no. 2(12),  73–76  mathnet 1
2010
10. V. N. Salii, “On the frame of an automaton”, Prikl. Diskr. Mat., 2010, no. supplement № 3,  98–99  mathnet
11. V. N. Salii, “Frame of an automaton”, Prikl. Diskr. Mat., 2010, no. 1(7),  63–67  mathnet 3
2009
12. V. N. Salii, “Automata all of whose congruences are inner”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 9,  36–45  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 53:9 (2009), 29–37 2
2008
13. V. N. Salii, “Minimal primitive extensions of oriented graphs”, Prikl. Diskr. Mat., 2008, no. 1(1),  116–119  mathnet 7
2005
14. V. N. Salii, “Optimization in Boolean-valued networks”, Diskr. Mat., 17:1 (2005),  141–146  mathnet  mathscinet  zmath  elib; Discrete Math. Appl., 15:2 (2005), 195–200 8
2002
15. V. N. Salii, “Idempotent semigroups with the transitive commutativity relation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 1,  64–70  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 46:1 (2002), 62–67 1
2001
16. V. N. Salii, “Quasi-Boolean Powers of Elementary 2-Groups”, Mat. Zametki, 69:6 (2001),  899–905  mathnet  mathscinet  zmath; Math. Notes, 69:6 (2001), 820–826  isi
1999
17. V. N. Salii, “Quasi-Boolean degrees of semilattices”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 7,  54–60  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 43:7 (1999), 51–57 1
18. V. N. Salii, “Quasi-Boolean powers of elementary Abelian $p$-groups”, Mat. Zametki, 66:2 (1999),  264–274  mathnet  mathscinet  zmath; Math. Notes, 66:2 (1999), 208–216  isi 2
1994
19. V. N. Salii, “Quasi-Boolean powers of singular semigroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 11,  67–74  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:11 (1994), 64–71 3
1980
20. V. N. Salii, “Some conditions for distributivity of a lattice with unique complements”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, no. 5,  47–49  mathnet  mathscinet  zmath
1973
21. V. N. Salii, “Boolean-valued algebras”, Mat. Sb. (N.S.), 92(134):4(12) (1973),  550–563  mathnet  mathscinet  zmath; Math. USSR-Sb., 21:4 (1973), 544–557
1972
22. V. N. Salii, “A compactly generated lattice with unique complements is distributive”, Mat. Zametki, 12:5 (1972),  617–620  mathnet  mathscinet  zmath; Math. Notes, 12:5 (1972), 806–807
1969
23. V. N. Salii, “Relativized semigroups of transformations containing the first projective relation $\underset1\chi$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 8,  89–103  mathnet  mathscinet  zmath 1
24. V. N. Salii, “Equationally normal varieties of semigroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 5,  61–68  mathnet  mathscinet  zmath 1
25. V. N. Salii, “On the theory of inversive semirings”, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 3,  52–60  mathnet  mathscinet  zmath
1968
26. V. N. Salii, “Transformative semigroups $(\mathfrak{G},\circ,\xi,\chi_1,\chi_2)$”, Dokl. Akad. Nauk SSSR, 179:1 (1968),  30–33  mathnet  mathscinet  zmath
27. V. N. Salii, “Nonassociative systems connected with $\mathfrack L$-transformations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1968, no. 3,  86–95  mathnet  mathscinet  zmath
1967
28. V. N. Salii, “Semigroups of $\mathfrak{L}$-sets”, Sibirsk. Mat. Zh., 8:3 (1967),  659–668  mathnet  mathscinet  zmath; Siberian Math. J., 8:3 (1967), 488–495 1
1966
29. V. N. Salii, “Projective semigroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1966, no. 3,  144–149  mathnet  mathscinet  zmath 1
1965
30. V. N. Salii, “Binary $\mathfrak L$-relations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1965, no. 1,  133–145  mathnet  mathscinet  zmath

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