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Vechtomov, Evgeniy Mikhailovich
Statistics Math-Net.Ru
Total publications: 51
Scientific articles: 50
Presentations: 2

Number of views:
This page:7176
Abstract pages:16942
Full texts:7363
References:1696
Professor
Doctor of physico-mathematical sciences (1994)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
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.

https://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 Citations
2023
1. E.M. Vechtomov, A. A. Petrov, “Multiplicatively idempotent semirings with annihilator condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 3,  29–40  mathnet
2. E.M. Vechtomov, V. V. Chermnykh, “Lambek functional representation of generalized symmetric semirings”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 2,  26–35  mathnet; Russian Math. (Iz. VUZ), 67:2 (2023), 23–31
3. V. I. Varankina, E.M. Vechtomov, “Semigroups of Relatively Continuous Binary Relations and Their Isomorphisms”, Mat. Zametki, 113:6 (2023),  807–819  mathnet  mathscinet; Math. Notes, 113:6 (2023), 760–769  scopus
4. E.M. Vechtomov, E. N. Lubyagina, “Semirings of continuous partial numerical functions with extended addition”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:1 (2023),  56–66  mathnet  mathscinet  elib
2022
5. E. M. Vechtomov, E. N. Lubyagina, “Subalgebras in semirings of continuous partial real-valued functions”, Fundam. Prikl. Mat., 24:1 (2022),  125–140  mathnet; J. Math. Sci., 269:5 (2023), 697–707
6. E. M. Vechtomov, A. A. Petrov, “Multiplicatively Idempotent Semirings in which All Congruences Are Ideal”, Mat. Zametki, 112:3 (2022),  376–383  mathnet  mathscinet; Math. Notes, 112:3 (2022), 382–387  scopus 1
7. E. M. Vechtomov, A. A. Petrov, “Completely Prime Ideals in Multiplicatively Idempotent Semirings”, Mat. Zametki, 111:4 (2022),  494–505  mathnet  mathscinet; Math. Notes, 111:4 (2022), 515–524  scopus 3
2020
8. E. M. Vechtomov, D. V. Chuprakov, “Finite cyclic semirings with semilattice additive operation defined by two-generated ideal of natural numbers”, Chebyshevskii Sb., 21:1 (2020),  82–100  mathnet
2016
9. 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
10. 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 4
2015
11. 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 2
12. 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 1
13. 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 5
2014
14. 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 1
2013
15. 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 7
16. 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 1
2012
17. 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 2
18. 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 3
19. 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, no. 1,  87–91  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:1 (2012), 79–82  scopus 4
2011
20. 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, no. 2,  12–18  mathnet 3
2010
21. 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 6
2009
22. 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 2
23. E. M. Vechtomov, A. V. Cheraneva, “Semifields with generator”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 3,  25–33  mathnet  elib 1
2008
24. 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 6
25. 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 3
26. 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 1
27. 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 3
2007
28. 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 2
1998
29. 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 19
1997
30. 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 13
1996
31. E. M. Vechtomov, “Distributive lattices which have chain functional representation”, Fundam. Prikl. Mat., 2:1 (1996),  93–102  mathnet  mathscinet  zmath 4
32. E. M. Vechtomov, “Divisibility in the rings $C(X,F)$ of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 1,  7–16  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 40:1 (1996), 5–14
33. 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 1
1994
34. 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 1
35. 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
36. 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 6
37. 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
38. 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 2
1992
39. 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 5
1991
40. 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 10
1990
41. 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 15
42. 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 2
1986
43. E. M. Vechtomov, “Boolean rings”, Mat. Zametki, 39:2 (1986),  182–185  mathnet  mathscinet  zmath; Math. Notes, 39:2 (1986), 101–103  isi 4
1983
44. 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 5
1982
45. 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
46. E. M. Vechtomov, “Ideals of rings of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1981, no. 1,  3–10  mathnet  mathscinet  zmath 1
1980
47. 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
48. 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 1
49. E. M. Vechtomov, “The isomorphism of multiplicative semigroups of rings of continuous functions”, Sibirsk. Mat. Zh., 19:4 (1978),  759–771  mathnet  mathscinet  zmath; Siberian Math. J., 19:4 (1978), 536–545  isi 2
1997
50. 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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