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Vechtomov, Evgenii Mikhailovich

Statistics Math-Net.Ru
Total publications: 41
Scientific articles: 40
Presentations: 2

Number of views:
This page:4769
Abstract pages:11015
Full texts:3947
References:905
Professor
Doctor of physico-mathematical sciences (1994)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 15.05.1953
E-mail: , ,
Keywords: rings of continuous functions; topological spaces; functional representations of rings; ideals, congruencies and subalgebras in semirings of continuous functions; theory of semirings.

Subject:

Elementary properties of divisibility in rings of continuous functions with values in disconnected normed field were studied. The general theory of rings of continuous functions, connected with their maximal spectrum, was developed. It was applied for research of properties of ideals in rings and semirings of continuous functions. The problem of structural isomorphism of rings of continuous functions was solved. The theory of Abelian-regular positive semirings was constructed.

Biography

Graduated from Faculty of Mathematics of Kirov State Pedagogical Institute in 1974. Ph. D. thesis was defended in 1979. D. Sci. thesis was defended in 1994. A list of my works contains 170 titles. Since 1994 I has led the scientific seminar on functional algebra at Vyatka State Humanities University.

Member-correspondent of Russian Academy Natural Sciences. Soros professor in 1998–2001.

   
Main publications:
  • Vechtomov E. M. Rings of continuous functions with values in a topological field // J. Math. Sciences. 1996, 78(6), 702–753.

http://www.mathnet.ru/eng/person17289
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/196261

Publications in Math-Net.Ru
2016
1. E. M. Vechtomov, A. A. Petrov, “Pseudocomplements in the lattice of subvarieties of a variety of multiplicatively idempotent semirings”, Fundam. Prikl. Mat., 21:3 (2016),  107–120  mathnet; J. Math. Sci., 237:3 (2019), 410–419
2. E. M. Vechtomov, A. V. Mikhalev, V. V. Sidorov, “Semirings of continuous functions”, Fundam. Prikl. Mat., 21:2 (2016),  53–131  mathnet; J. Math. Sci., 237:2 (2019), 191–244
2015
3. E. M. Vechtomov, N. V. Shalaginova, “Semirings of continuous $(0,\infty]$-valued functions”, Fundam. Prikl. Mat., 20:6 (2015),  43–64  mathnet  elib; J. Math. Sci., 233:1 (2018), 28–41
4. E. M. Vechtomov, I. V. Orlova, “Cyclic semirings with nonidempotent noncommutative addition”, Fundam. Prikl. Mat., 20:6 (2015),  17–41  mathnet  elib; J. Math. Sci., 233:1 (2018), 10–27
5. E. M. Vechtomov, V. V. Sidorov, “Definability of Hewitt spaces by the lattices of subalgebras of semifields of continuous positive functions with max-plus”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:3 (2015),  78–88  mathnet  mathscinet  elib
2014
6. E. M. Vechtomov, A. A. Petrov, “Variety of semirings generated by two-element semirings with commutative idempotent multiplication”, Chebyshevskii Sb., 15:3 (2014),  12–30  mathnet
2013
7. E. M. Vechtomov, A. A. Petrov, “Multiplicatively idempotent semirings”, Fundam. Prikl. Mat., 18:4 (2013),  41–70  mathnet  mathscinet; J. Math. Sci., 206:6 (2015), 634–653  scopus
8. E. M. Vechtomov, E. N. Lubyagina, “Closed ideals and closed congruences of semirings of $[0,1]$-valued functions with topology of pointwise convergence”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013),  83–93  mathnet  mathscinet  elib
2012
9. E. M. Vechtomov, E. N. Lubyagina, “The semiring of continous $[0,1]$-valued functions”, Fundam. Prikl. Mat., 17:4 (2012),  53–82  mathnet; J. Math. Sci., 191:5 (2013), 633–653  scopus
10. E. M. Vechtomov, I. V. Lubyagina, “Cyclic semirings with idempotent noncommutative addition”, Fundam. Prikl. Mat., 17:1 (2012),  33–52  mathnet; J. Math. Sci., 185:3 (2012), 367–380  scopus
11. E. M. Vechtomov, E. N. Lubyagina, “The determinability of compacts by lattices of ideals and congruencies of semirings of continuous $[0,1]$-valued functions on them”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, 1,  87–91  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:1 (2012), 79–82  scopus
2011
12. E. M. Vechtomov, E. N. Lubiagina, “About prime ideals in semirings of continuous function with values in unit segment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, 2,  12–18  mathnet
2010
13. E. M. Vechtomov, V. V. Sidorov, “Isomorphisms of lattices of subalgebras of semirings of continuous nonnegative functions”, Fundam. Prikl. Mat., 16:3 (2010),  63–103  mathnet  mathscinet; J. Math. Sci., 177:6 (2011), 817–846  scopus
2009
14. E. M. Vechtomov, D. V. Chuprakov, “Extension of Congruences on Semirings of Continuous Functions”, Mat. Zametki, 85:6 (2009),  803–816  mathnet  mathscinet  zmath; Math. Notes, 85:6 (2009), 767–779  isi  scopus
15. E. M. Vechtomov, A. V. Cheraneva, “Semifields with generator”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, 3,  25–33  mathnet  elib
2008
16. E. M. Vechtomov, A. V. Cheraneva, “Semifields and their properties”, Fundam. Prikl. Mat., 14:5 (2008),  3–54  mathnet  mathscinet  elib; J. Math. Sci., 163:6 (2009), 625–661  elib  scopus
17. E. M. Vechtomov, D. V. Chuprakov, “The principal kernels of semifields of continuous positive functions”, Fundam. Prikl. Mat., 14:4 (2008),  87–107  mathnet  mathscinet  elib; J. Math. Sci., 163:5 (2009), 500–514  elib  scopus
18. E. M. Vechtomov, M. A. Lukin, “Semirings which are the unions of a ring and a semifield”, Uspekhi Mat. Nauk, 63:6(384) (2008),  159–160  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:6 (2008), 1152–1153  isi  elib  scopus
19. E. M. Vechtomov, A. V. Cheraneva, “On the theory of semidivision rings”, Uspekhi Mat. Nauk, 63:2(380) (2008),  161–162  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:2 (2008), 391–393  isi  scopus
2007
20. E. M. Vechtomov, O. V. Starostina, “Structure of abelian regular positive semirings”, Uspekhi Mat. Nauk, 62:1(373) (2007),  199–200  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:1 (2007), 199–201  isi  elib  scopus
1998
21. V. I. Varankina, E. M. Vechtomov, I. A. Semenova, “Semirings of continuous nonnegative functions: divisibility, ideals, congruences”, Fundam. Prikl. Mat., 4:2 (1998),  493–510  mathnet  mathscinet  zmath
1997
22. E. M. Vechtomov, “Lattice of subalgebras of the ring of continuous functions and Hewitt spaces”, Mat. Zametki, 62:5 (1997),  687–693  mathnet  mathscinet  zmath; Math. Notes, 62:5 (1997), 575–580  isi
1996
23. E. M. Vechtomov, “Distributive lattices which have chain functional representation”, Fundam. Prikl. Mat., 2:1 (1996),  93–102  mathnet  mathscinet  zmath
24. E. M. Vechtomov, “Divisibility in the rings $C(X,F)$ of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, 1,  7–16  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:1 (1996), 5–14
25. E. M. Vechtomov, M. N. Smirnova, “A duality for topological semirings of continuous functions”, Uspekhi Mat. Nauk, 51:3(309) (1996),  187–188  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:3 (1996), 571–572  isi  scopus
1994
26. E. M. Vechtomov, “Rings of continuous functions and their maximal spectra”, Mat. Zametki, 55:6 (1994),  32–49  mathnet  mathscinet  zmath; Math. Notes, 55:6 (1994), 568–579  isi
27. E. M. Vechtomov, “On the general theory of rings of continuous functions”, Uspekhi Mat. Nauk, 49:3(297) (1994),  177–178  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:3 (1994), 202–204  isi
1993
28. E. M. Vechtomov, “Annihilator characterizations of Boolean rings and Boolean lattices”, Mat. Zametki, 53:2 (1993),  15–24  mathnet  mathscinet  zmath; Math. Notes, 53:2 (1993), 124–129  isi
29. E. M. Vechtomov, “Rings of continuous functions and sheaves of rings”, Uspekhi Mat. Nauk, 48:5(293) (1993),  167–168  mathnet  mathscinet  zmath; Russian Math. Surveys, 48:5 (1993), 187–188
30. E. M. Vechtomov, “Rings of continuous functions and the theory of Gel'fand”, Uspekhi Mat. Nauk, 48:1(289) (1993),  163–164  mathnet  mathscinet  zmath; Russian Math. Surveys, 48:1 (1993), 199–200  isi
1992
31. E. M. Vechtomov, “On the Gel'fand–Kolmogorov theorem on maximal ideals of rings of continuous functions”, Uspekhi Mat. Nauk, 47:5(287) (1992),  171–172  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:5 (1992), 207–208  isi
1991
32. E. M. Vechtomov, “Rings of continuous functions. Algebraic aspects”, Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 29 (1991),  119–191  mathnet  mathscinet  zmath; J. Math. Sci., 71:2 (1994), 2364–2408
1990
33. E. M. Vechtomov, “Questions on the determination of topological spaces by algebraic systems of continuous functions”, Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 28 (1990),  3–46  mathnet  mathscinet  zmath; J. Soviet Math., 53:2 (1991), 123–147
34. E. M. Vechtomov, “On semigroups of continuous partial functions of topological spaces”, Uspekhi Mat. Nauk, 45:4(274) (1990),  143–144  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:4 (1990), 192–193  isi
1986
35. E. M. Vechtomov, “Boolean rings”, Mat. Zametki, 39:2 (1986),  182–185  mathnet  mathscinet  zmath; Math. Notes, 39:2 (1986), 101–103  isi
1983
36. E. M. Vechtomov, “Distributive rings of continuous functions and $F$-spaces”, Mat. Zametki, 34:3 (1983),  321–332  mathnet  mathscinet  zmath; Math. Notes, 34:3 (1983), 643–648  isi
1982
37. E. M. Vechtomov, “On the module of functions with compact support over a ring of continuous functions”, Uspekhi Mat. Nauk, 37:4(226) (1982),  151–152  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:4 (1982), 147–148  isi
1981
38. E. M. Vechtomov, “Ideals of rings of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1981, 1,  3–10  mathnet  mathscinet  zmath
1980
39. E. M. Vechtomov, “Module of all functions over the ring of continuous functions”, Mat. Zametki, 28:4 (1980),  481–490  mathnet  mathscinet  zmath; Math. Notes, 28:4 (1980), 701–705  isi
1978
40. E. M. Vechtomov, “Isomorphism of the multiplicative semigroups of algebras of continuous functions with compact support”, Uspekhi Mat. Nauk, 33:5(203) (1978),  175–176  mathnet  mathscinet  zmath; Russian Math. Surveys, 33:5 (1978), 213–214

1997
41. E. M. Vechtomov, “Correction of the paper “Distributive lattices which have chain functional representation””, Fundam. Prikl. Mat., 3:1 (1997),  315  mathnet  mathscinet

Presentations in Math-Net.Ru
1. Determination of $T_1$-spaces by a lattice of subalgebras with identity semirings of continuous partial numerical functions
E. M. Vechtomov, E. N. Lubyagina
XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich
May 29, 2018 17:30
2. To the theory of multiplicative cyclic semirings
D. V. Chuprakov, E. M. Vechtomov, I. V. Orlova
XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich
May 29, 2018 15:00

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