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Uspekhi Mat. Nauk, 1998, Volume 53, Issue 4(322), Pages 3–76 (Mi umn56)  

This article is cited in 26 scientific papers (total in 26 papers)

Serre's quantum problem

V. A. Artamonov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

DOI: https://doi.org/10.4213/rm56

Full text: PDF file (662 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1998, 53:4, 657–730

Bibliographic databases:

UDC: 512.55
MSC: 81Rxx, 13M10
Received: 04.12.1996

Citation: V. A. Artamonov, “Serre's quantum problem”, Uspekhi Mat. Nauk, 53:4(322) (1998), 3–76; Russian Math. Surveys, 53:4 (1998), 657–730

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. V. A. Artamonov, “The skew field of rational quantum functions”, Russian Math. Surveys, 54:4 (1999), 825–827  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Artamonov, “General quantum polynomials: irreducible modules and Morita equivalence”, Izv. Math., 63:5 (1999), 847–880  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. M. Maksimov, “A generalization of the ring of Ore skew polynomials”, Russian Math. Surveys, 55:4 (2000), 817–818  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. A. Artamonov, “Automorphisms of the skew field of rational quantum functions”, Sb. Math., 191:12 (2000), 1749–1771  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Artamonov V.A., “Quantum division ring”, Formal Power Series and Algebraic Combinatorics, 2000, 402–413  crossref  mathscinet  zmath  isi
    6. Artamonov V.A., “General quantum polynomials”, Algebra, 2000, 35–48  crossref  mathscinet  zmath  isi
    7. Artamonov, VA, “Homological properties of quantum polynomials”, Algebras and Representation Theory, 4:3 (2001), 219  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Li, HS, “Noncommutative Grobner bases and filtered-graded transfer”, Noncommunicative Grobner Bases and Filtered-Graded Transfer, 1795 (2002), 1  crossref  mathscinet  adsnasa  isi
    9. Gago-Vargas J., “Constructions in $R[x_1,…,x_n]$: applications to $K$-theory”, J. Pure Appl. Algebra, 171:2-3 (2002), 185–196  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Artamonov V.A., “Actions of Hopf algebras on quantum polynomials”, Representations of Algebras, Proceedings, Lecture Notes in Pure and Applied Mathematics, 224, 2002, 11–20  mathscinet  zmath  isi
    11. Antoniou L.E., Iyudu N.K., Wisbauer R., “On Serre's problem for RIT algebras”, Comm. Algebra, 31:12 (2003), 6037–6050  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. V. M. Maximov, “Canonical forms of skew polynomial rings”, Journal of Mathematical Sciences (New York), 126:2 (2005), 1064  crossref  mathscinet
    13. E. N. Shirikov, “Jordanian plane”, J. Math. Sci., 154:2 (2008), 270–278  mathnet  crossref  mathscinet  zmath  elib  elib
    14. E. N. Shirikov, “The Jordan Plane over a Field of Positive Characteristic”, Math. Notes, 82:2 (2007), 238–256  mathnet  crossref  crossref  mathscinet  isi  elib
    15. S. N. Tronin, “On retracts and retractions of free modules over graded rings”, Russian Math. (Iz. VUZ), 51:7 (2007), 68–71  mathnet  crossref  mathscinet  zmath  elib
    16. Shirikov E.N., “Irreducible modules over a Jordan plane over a field of characteristic zero”, Moscow Univ. Math. Bull., 64:2 (2009), 47–50  crossref  mathscinet  zmath  elib  elib  scopus
    17. ASHISH GUPTA, “MODULES OVER QUANTUM Laurent POLYNOMIALS”, J. Aust. Math. Soc, 91:03 (2012), 323  crossref  mathscinet  isi  scopus  scopus
    18. Johnson F.E.A., “Stably Free Cancellation for Group Rings of Cyclic and Dihedral Type”, Q. J. Math., 63:3 (2012), 623–635  crossref  mathscinet  zmath  isi  scopus
    19. Oswaldo Lezama, J.P.ablo Acosta, Cristian Chaparro, Ingrid Ojeda, César Venegas, “ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS”, Asian-European J. Math, 2013, 1350061  crossref  mathscinet  zmath  scopus  scopus
    20. Oswaldo Lezama, Armando Reyes, “Some Homological Properties of SkewPBWExtensions”, Communications in Algebra, 42:3 (2014), 1200  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Lezama O., Pablo Acosta J., Reyes Villamil M.A., “Prime Ideals of Skew Pbw Extensions”, 56, no. 2, 2015, 39–55  mathscinet  zmath  isi
    22. Lezama O., Gallego C., “Projective modules and Gröbner bases for skew PBW extensions”, Diss. Math., 2017, no. 521, 1–50  crossref  mathscinet  zmath  isi  scopus
    23. Trans. Moscow Math. Soc., 78 (2017), 235–256  mathnet  crossref  elib
    24. Belov A.K., Razavinia F., Zhang W., “Bergman'S Centralizer Theorem and Quantization”, Commun. Algebr., 46:5 (2018), 2123–2129  crossref  mathscinet  zmath  isi  scopus  scopus
    25. Fajardo W., Lezama O., “Elementary Matrix-Computational Proof of Quillen-Suslin Theorem For Ore Extensions”, Fundam. Inform., 164:1 (2019), 41–59  crossref  mathscinet  isi  scopus
    26. Fajardo W., “A Computational Maple Library For Skew Pbw Extensions”, Fundam. Inform., 167:3 (2019), 159–191  crossref  isi
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