Ir al contenido

Documat


On the importance of being primitive

  • Bell, Jason [1]
    1. [1] University of Waterloo

      University of Waterloo

      Canadá

  • Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 53, Nº. Extra 1, 2019 (Ejemplar dedicado a: Suplemento), págs. 87-112
  • Idioma: inglés
  • DOI: 10.15446/recolma.v53nsupl.84009
  • Enlaces
  • Resumen
    • español

      Hacemos un breve estudio de la primitividad en la teoría de anillos y, en particular, veremos caracterizaciones de ideales primitivos en el espectro primo para varias clases de anillos.

    • English

      We give a brief survey of primitivity in ring theory and in particular look at characterizations of primitive ideals in the prime spectrum for various classes of rings.

  • Referencias bibliográficas
    • G. Abrams, J. P. Bell, and K. M Rangaswamy, The Dixmier-Moeglin equivalence for Leavitt path algebras, Algebr. Represent. Theory 15 (2002),...
    • M. Artin and J. T. Stafford, Noncommutative graded domains with quadratic growth, Invent. Math. 122 (1995), no. 2, 231-276.
    • Y. A. Bachturin, Identities in the universal envelopes of Lie algebras. Collection of articles dedicated to the memory of Hanna Neumann, IX,...
    • J. Bell, S. Launois, and B. Nolan, A strong Dixmier-Moeglin equivalence for quantum Schubert cells, J. Algebra 487 (2017), 269-293.
    • J. Bell, S. Launois, O. León Sánchez, and R. Moosa, Poisson algebras via model theory and differential-algebraic geometry, J. Eur. Math. Soc....
    • J. Bell, D. Rogalski, and S. J. Sierra, The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings, Israel J. Math. 180 (2010),...
    • J. Bell, O. León Sánchez, and R. Moosa, D-groups and the Dixmier-Moeglin equivalence, Algebra Number Theory 12 (2018), no. 2, 343-378.
    • J. P. Bell and D. Ghioca, Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations, Adv. Math. 349 (2019),...
    • J. P. Bell and W. H. Leung, The Dixmier-Moeglin equivalence for co-commutative Hopf algebras of finite Gelfand-Kirillov dimension, Algebr....
    • J. P. Bell, X. Wang, and D. Yee, The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra, J. Algebra 534 (2019),...
    • J. P. Bell, K. Wu, and S. Wu, The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions, Groups, rings, group rings, and...
    • G. M. Bergman, A ring primitive on the right but not on the left, Proc. Amer. Math. Soc. 15 (1964), 473-475.
    • K. Brown, S. O'Hagan, J. Zhang, and G. Zhuang, Connected Hopf algebras and iterated Ore extensions, J. Pure Appl. Algebra 219 (2015),...
    • K. A. Brown, The Nullstellensatz for certain group rings, J. London Math. Soc. 26 (1982), no. 3, 425-434.
    • K. A. Brown, P. A.A.B. Carvalho, and J. Matczuk, Simple modules and their essential extensions for skew polynomial rings, Preprint, available...
    • K. A. Brown and P. Gilmartin, Hopf algebras under finiteness conditions, Palest. J. Math. 3 (2014), Special issue, 356-365.
    • K. A. Brown and K. R. Goodearl, Lectures on algebraic quantum groups, Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel,...
    • K. A. Brown and I. Gordon, Poisson orders, symplectic reflection algebras and representation theory, J. Reine Angew. Math. 559 (2003), 193-216.
    • K. Casteels, Quantum matrices by paths, Algebra Number Theory 8 (2014), no. 8, 1857-19129.
    • G. Cauchon, Effacement des dérivations et spectres premiers des algèbres quantiques, J. Algebra 260 (2003), no. 2, 476-518.
    • J. Dixmier, Idéaux primitifs dans les algèbres enveloppantes, J. Algebra 48 (1977), 96-112.
    • D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995.
    • K. R. Goodearl and R. B. Warfield Jr., Primitivity in differential operator rings, Math. Z. 180 (1982), no. 4, 503-523.
    • K. R. Goodearl and R. B. Warfield Jr., An introduction to noncommutative noetherian rings, Second edition. London Mathematical Society Student...
    • K. R. Goodearl and S. Launois, The Dixmier-Moeglin equivalence and a Gelfand-Kirillov problem for Poisson polynomial algebras, Bull. Soc....
    • K. R. Goodearl, S. Launois, and T. H. Lenagan, Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic...
    • K. R. Goodearl and E. S. Letzter, The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras, Trans. Amer. Math....
    • K. R. Goodearl and J. J. Zhang, Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two, J. Algebra 324 (2010), no. 11, 3131-3168.
    • R. S. Irving, Noetherian algebras and nullstellensatz, Séminaire d'Algèbre Paul Dubreil 31 me année (Paris, 1977-1978). Lecture Notes...
    • R. S. Irving, Primitive ideals of certain Noetherian algebras, Math. Z. 169 (1979), no. 1, 77-92.
    • R. S. Irving, Primitive Noetherian algebras with big centers, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1587-1593.
    • N. Jacobson, Structure theory for algebraic algebras of bounded degree, Ann. Math. 46 (1945), 695-707.
    • A. V. Jategaonkar, Relative Krull dimension and prime ideals in right Noetherian rings, Comm. Algebra 2 (1974), 429-468.
    • D. A. Jordan, Primitive Ore extensions, Glasgow Math. J. 18 (1977), no. 1, 93-97.
    • D. A. Jordan, Primitivity in skew Laurent polynomial rings and related rings, Math. Z. 213 (1993), no. 3, 353-371.
    • D. A. Jordan and S.-Q. Oh, Poisson spectra in polynomial algebras, J. Algebra 400 (2014), 56-71.
    • M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3, 157-216.
    • G. R. Krause and T. H. Lenagan, Growth of algebras and gelfand-kirillov dimension, Revised edition. Graduate Studies in Mathematics, 22. American...
    • S. Launois and C. Lecoutre, Poisson deleting derivations algorithm and Poisson spectrum, Comm. Algebra 45 (2017), no. 3, 1294-1313.
    • A. Leroy and J. Matczuk, Primitivity of skew polynomial and skew Laurent polynomial rings, Comm. Algebra 24 (1996), no. 7, 2271-2284.
    • A. Leroy and J. Matczuk, On q-skew iterated Ore extensions satisfying a polynomial identity, J. Algebra Appl. 10 (2011), no. 4, 771-781.
    • E. Letzter, Primitive ideals in finite extensions of Noetherian rings, J. London Math. Soc. 39 (1989), no. 2-3, 427-435.
    • M. Lorenz, Primitive ideals of group algebras of supersoluble groups, Math. Ann. 225 (1977), no. 2, 115-122.
    • M. Lorenz, Group actions and rational ideals, Algebra Number Theory 2 (2008), no. 4, 467-499.
    • M. Lorenz, Algebraic group actions on noncommutative spectra, Transform. Groups 14 (2009), no. 3, 649-675.
    • M. Lorenz, On the stratification of noncommutative prime spectra, Proc. Amer. Math. Soc. 142 (2014), no. 9, 3013-3017.
    • C. Moeglin, Idéaux bilatères des algèbres enveloppantes, Bull. Soc. Math. France 108 (1980), 143-186.
    • C. Moeglin and R. Rentschler, Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante, Bull....
    • C. Moeglin and R. Rentschler, Idéaux g-rationnels, Rang de Goldie. Unpublished manuscript, 1986.
    • S.-Q. Oh, Quantum and Poisson structures of multi-parameter symplectic and Euclidean spaces, J. Algebra 319 (2008), no. 11, 4485-4535.
    • , Poisson Hopf algebra related to a twisted quantum group, Comm. Algebra 45 (2017), no. 1, 76-104.
    • L. H. Rowen, Ring theory. vol. ii., Pure and Applied Mathematics, 128. Academic Press, Inc., Boston, MA, 1988.
    • L. H. Rowen, Graduate algebra: noncommutative view, Graduate Studies in Mathematics, 91. American Mathematical Society, Providence, RI, 2008.
    • R. L. Snider, Primitive ideals in group rings of polycyclic groups, Proc. Amer. Math. Soc. 57 (1976), no. 1, 8-10.
    • N. Vonessen, Actions of algebraic groups on the spectrum of rational ideals, J. Algebra 182 (1996), no. 2, 383-400.
    • N. Vonessen, Actions of algebraic groups on the spectrum of rational ideals. II., J. Algebra 208 (1998), no. 1, 216-261.
    • M. Yakimov, Invariant prime ideals in quantizations of nilpotent Lie algebras, Proc. Lond. Math. Soc.(3) 101 (2010), no. 2, 454-476.
    • M. Yakimov, On the spectra of quantum groups, Mem. Amer. Math. Soc. 229 (2014), no. 1078.
    • A. E. Zalesskii, The irreducible representations of finitely generated nilpotent groups without torsion, Mat. Zametki 9 (1971), 199-210.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno