Books

  • S. Montgomery, L. Rowen and H.-J. Schneider (co-editors), Special Issue of Communications in Algebra in honor of Miriam Cohen, vol. 39, no. 12, Taylor and Francis 2011.
  • New Directions in Hopf Algebras (co-editor with H.-J. Schneider), MSRI Publications, vol. 43, Cambridge University Press, 2002
  • Hopf Algebras and Their Actions on Rings, CBMS Lecture Notes vol 82, American Math Society, Providence, RI, 1993 (238 pages).
  • Advances in Hopf Algebras (co-editor with Jeffrey Bergen), Lecture Notes in Pure and Applied Math 158, Marcel Dekker, 1994.
  • Non-Commutative Rings (co-editor with L. W. Small), MSRI Publications, vol 24, Springer-Verlag, 1992.
  • Group Actions on Rings (editor), Proceedings of Joint Summer Research Conference, AMS Contemporary Math, vol 43, AMS 1985.
  • Fixed Rings of Finite Automorphism Groups of Associative Rings , Lecture Notes in Math 818, Springer-Verlag, New York, 1980.
  • Selected Papers on Algebra (co-chair of editorial committee), Raymond W. Brink Selected Mathematical Papers, vol 3, Mathematical Association of America, Washington DC, 1977.

Papers

  • A. Mejia Casrano, S. Montgomery, S. Natale, M. Vega, and C. Walton, Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension p3 and pq2, submitted (arXiv:1610.03810).
  • S. Montgomery, M. Vega, and S. Witherspoon, Hopf automorphisms and twisted extensions, Journal of Algebra and Applications 15, No 6, (2016) (14 pages).
  • M. Iovanov, G. Mason, and S. Montgomery, F SZ-groups and Frobenius-Schur indicators of quantum doubles, Math Research Letters 21 (2014), 757-779.
  • A. Jedwab and S. Montgomery, Modular representations and indicators for bismash products, J. Algebra 377 (2013), 281-297. 21
  • Y. Kashina, S. Montgomery, and S-H. Ng, On the trace of the antipode and higherindicators, Israel J. Math 188 (2012), 57-90.
  • A. Jedwab and S. Montgomery, A q-identity related to a comodule, Communications in Algebra 39 (2011), 4669-4678 (Special issue in honor of Miriam Cohen).
  • S. Montgomery, Hopf Galois theory: a survey, in New Topological Contexts for Galois Theory and Algebraic Geometry (A. Baker and B. Richter, editors), Geometry and Topology Monographs 16 (2009), 367-400.
  • Y. Bahturin, M. Kochetov, and S. Montgomery, Group gradings on simple Lie algebras in finite characteristic, AMS Proceedings 137 (2009), 1245 – 1254.
  • R. M. Guralnick and S. Montgomery, Frobenius-Schur indicators for subgroups and the Drinfel’d double of Weyl groups, AMS Transactions 361 (2009), 3611-3632.
  • A. Jedwab and S. Montgomery, Representations of some Hopf algebras associated to the symmetric group Sn, Algebras and Representation Theory 12 (2009), 1-17.
  • V. Linchenko and S. Montgomery, Semiprime smash products and H-stable prime radicals for PI-algebras, AMS Proceedings 135 (2007), 3091-3098.
  • R. Landers, S. Montgomery, and P. Schauenburg, Hopf powers and orders for some bismash products, J. Pure and Applied Algebra 205 (2006), 156-188.
  • V. Linchenko, S. Montgomery and L. W. Small, Stable Jacobson Radicals and Semiprime Smash Products, London Math. Soc. Bulletin 37 (2005), 860-872.
  • S. Montgomery, Algebra properties invariant under twisting, in Hopf Algebras in Noncommutative Geometry and Physics (S. Caenepeel and F. Van Oystaeyen, editors), Lecture Notes in Pure and Applied Math 239, Marcel Dekker, New York, 2005, 61-75.
  • S. Montgomery and H.-J. Schneider, Krull relations in Hopf Galois extensions: lifting and twisting, J. Algebra 288 (2005), 364-383.
  • S. Montgomery, Primitive ideals in Hopf Galois extensions, in Algebraic Structures and their Representations, XV Colloquio Latinamericano, Cocoyoc, Mexico (Jose de la Pe˜na, E. Vallejo, and N. Atakishiyev, Editors), AMS Contemporary Math 376 (2005), 333-344.
  • Y. Bahturin, S. Montgomery, and M. Zaicev, Generalized Lie solvability of associative algebras, Groups, Rings, Lie, and Hopf Algebras (Yu. Bahturin, editor), Proceedings of the 2001 St. John’s Conference, Kluwer, 2003, 1-23.
  • Y. Bahturin, M. Kochetov and S. Montgomery, Polycharacters of cocommutative Hopf algebras, Canadian Math Bulletin 45 (2002), 11-24.20
  • Y. Kashina, G. Mason and S. Montgomery, Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras, J. Algebra 251 (2002), 888-913.
  • S. Montgomery, Bicharacters, twistings, and Scheunert’s theorem for Hopf algebras (with Yu. Bahturin and D. Fischman), J. of Algebra 236 (2001), 246-276.
  • S. Montgomery and H.-J. Schneider, Skew-derivations of finite-dimensional algebras and actions of the double of the Taft Hopf algebra, Tsukuba J. of Math 25 (2001), 337-358.
  • S. Montgomery, Representation theory of finite-dimensional semisimple Hopf algebras, Algebra – Representation Theory (Constanta, 2000), K. W. Roggenkamp and M. Stefanescu, editors, NATO Sci. Ser. II Math. Phys. Chem. 28, Kluwer, Dordrecht, 2001, 189-218.
  • V. Linchenko and S. Montgomery, A Frobenius-Schur theorem for Hopf algebras, Algebras and Representation Theory 3 (2000), 347-355.
  • Y. Bahturin and S. Montgomery, PI-envelopes of Lie superalgebras, AMS Proceedings 127 (1999), 2829-2839.
  • S. Montgomery and H.-J. Schneider, Prime ideals in Hopf Galois extensions, Israel J Math 112 (1999), 187-235.
  • M. Cohen, D. Fischman and S. Montgomery, On Yetter-Drinfeld categories and Hcommutativity, Comm. in Algebra 27 (1999), 1321-1345.
  • S. Montgomery, Classifying finite-dimensional semisimple Hopf algebras, in Trends in the Representation Theory of Finite-Dimensional Algebras, E. Green and B. ZimmermannHuisgen, editors, AMS Contemporary Math. vol 229 (1998), 265-279.
  • S. Montgomery and L. W. Small, Nil subsets of graded algebras, AMS Proceedings 126 (1998), 653-656.
  • S. Montgomery and S. Witherspooon, Irreducible representations of crossed products, J. Pure and Applied Algebra 129 (1998), 315-326.
  • S. Montgomery, Constructing simple Lie superalgebras from associative graded algebras, J. of Algebra 195 (1997), 558 – 579.
  • D. Fischman, S. Montgomery and H.-J. Schneider, Frobenius extensions of subalgebras of Hopf algebras, AMS Transactions 349 (1997), 4857 – 4895.
  • W. Chin and S. Montgomery, Basic coalgebras, in Modular Interfaces: Modular Lie algebras, Quantum groups, and Lie superalgebras, V. Chari and I. Penkov, editors, AMS-International Press, vol 4, 1997, pp 41-47.
  • Y. Bahturin, D. Fischman and S. Montgomery, On the generalized Lie structure of
    associative algebras, Israel J. of Math. 96 (1996), 27-48.
  • S. Montgomery, Indecomposable coalgebras, simple comodules, and pointed Hopf algebras, AMS Proceedings 123 (1995), 2343-2351.
  • S. Montgomery and H.-J. Schneider, Hopf crossed products, rings of quotients and prime ideals, Advances in Math 112 (1995), 1-55.19
  • R. M. Guralnick and S. Montgomery, On invertible bimodules and automorphisms of non-commutative rings, AMS Transactions 341 (1994), 917-937.
  • D. Fischman and S. Montgomery, A Schur double centralizer theorem for cotriangular Hopf algebras and generalized Lie algebras, J. Algebra 168 (1994), 594-614.
  • S. Montgomery, Biinvertible actions of Hopf algebras, Israel J. of Math 83 (1993), 45-71.
  • S. Montgomery, Some remarks on filtrations of Hopf algebras, Comm. in Algebra 21 (1993), 999-1007.
  • S. Montgomery, Hopf Galois extensions, in Azumaya Algebras, Actions, and Modules, AMS Contemporary Math, Vol. 124, 1992, 129-140.
  • J. Bergen and S. Montgomery, Ideals and quotients in crossed products of Hopf algebras, J. Algebra 155 (1992), 374-396.
  • S. Montgomery, Book review of: Infinite Crossed Products, by D. S. Passman, AMS Bulletin 24 (1991), 391-402.
  • S. Montgomery and S. P. Smith, Skew derivations and Uq(sl(2)), Israel J. Math 72 (1990), 158-166.
  • M. Cohen, D. Fischman and S. Montgomery, Hopf Galois extensions, smash products, and Morita equivalence, J. of Algebra 133 (1990), 351-372.
  • S. Montgomery, A generalized Picard group for prime rings, in Topics in Algebra,
    Proceedings of the Algebra Semester 1988, Banach Center Publications Vol. 26, Part I, PWA – Polish Scientific Publishers, Warsaw 1990, 55-63.
  • R. J. Blattner and S. Montgomery, Crossed products and Galois extensions of Hopf algebras, Pacific J. Math, 137 (1989), 37-54.
  • R. Guralnick and S. Montgomery, Normalizing elements of the trace ring of generic matrices, Comm. in Algebra 27 (1989), 1805-1813.
  • S. Montgomery, Inner actions of Hopf algebras, in Ring Theory 1989 (in honor of S. A. Amitsur), Israel Math. Conference Proceedings, Weizmann Science Press, 1989, pp 141-149.
  • S. Montgomery, Prime ideals and group actions in non-commutative algebras, in Invariant Theory, AMS Contemporary Math. 88 (1989), 103-124.
  • S. Montgomery, Crossed products of Hopf algebras and enveloping algebras, in Perspectives in Ring Theory, Proceedings of NATO Workshop, Antwerp 1987, NATO ASI Series C, Vol. 233 Kluwer (1988), 253-268. 18
  • S. Montgomery, Progress on some problems about group actions, in Perspectives in Ring Theory, NATO ASI Series C, Vol 233, Kluwer, Dordrecht (1988), 269-274.
  • S. Montgomery and D. S. Passman, Algebraic analogs of the Connes spectrum, J. of Algebra 115 (1988) 92-124.
  • J. Bergen, S. Montgomery and D. S. Passman, Radicals of crossed products of enveloping algebra, Israel J. of Math. 59 (1987), 167-184.
  • S. Montgomery and D. S. Passman, Prime ideals in fixed rings of free algebras, Comm. in Algebra, 15 (1987), 2209-2234.
  • S. Montgomery and L. W. Small, Some remarks on affine rings, AMS Proceedings, 98 (1986), 537-544.
  • S. Montgomery and D. S. Passman, X-inner automorphisms of crossed products and semi-invariants of Hopf algebras, Israel J. Math. 55 (1986), 33-57.
  • R. J. Blattner, M. Cohen, and S. Montgomery, Crossed products and inner actions of Hopf algebras, AMS Transactions 298 (1986), 671-711.
  • J. W. Fisher and S. Montgomery, Invariants of finite cyclic groups acting on generic matrices, J. of Algebra 99 (1986), 430-437.
  • J. Bergen and S. Montgomery, Smash products and outer derivations, Israel J. of Math. 53 (1986), 321 – 345.
  • S. Montgomery, Duality for actions and coactions of groups, in Group Actions on Rings, AMS Contemporary Math, vol. 43 (1985), 191-207.
  • R. J. Blattner and S. Montgomery, A duality theorem for Hopf module algebras, J. of Algebra 95 (1985), 153-172.
  • S. Montgomery, Group actions on rings: some classical problems, in Methods in Ring Theory, F.van Oystaeyen, editor, NATO Advanced Study Institute in Ring Theory, Antwerp 1983, NATO ASI Series C, Vol. 129, Reidel (1984), 327-346.
  • Montgomery and D. S. Passman, Galois theory of prime rings, E. Noether 100th Birthday issue, J. Pure and Applied Algebra 31 (1984), 139-184. 17
  • S. Montgomery and L. W. Small, Integrality and prime ideals in fixed rings of PI rings, E. Noether 100th Birthday issue, J. Pure and Applied Algebra 31 (1984), 185-190.
  • S. Montgomery and D. S. Passman, Outer Galois theory of prime rings, Rocky Mountain J. Math. 14 (1984), 305-318.
  • S. Montgomery, von Neumann finiteness of tensor products of algebras, Comm. in Algebra 11 (1983), 595-610.
  • Montgomery, X-inner automorphisms of filtered algebras II, AMS Proceedings 87 (1983), 569-575.
  • W. S. Martindale, III and S. Montgomery, The normal closure of coproducts of domain, J. of Algebra 82 (1983), 1-17.
  • S. Montgomery, X-inner automorphisms of filtered algebras, AMS Proceedings 83 (1981), 263-268.
  • M. Lorenz, S. Montgomery and L. W. Small, Prime ideals in fixed rings II, Comm. in Algebra, 10 (1982), 449-455.
  • M. Cohen and S. Montgomery, Trace-like functions on rings with no nilpotent element, AMS Transactions 273 (1982), 131-145.
  • D. S. Passman and S. Montgomery, X-inner automorphisms of group rings II, Houston J. Math. 8 (1982), 537-544.
  • S. Montgomery, Trace functions and affine fixed rings for groups acting on non commutative rings, Seminaire d’Algebra Paul Dubreil et Marie-Paule Malliavin, Lecture Notes in Mathematics 924, Springer-Verlag (1982), 356-374.
  • S. Montgomery and L. W. Small, Fixed rings in Noetherian rings, London Math. Soc. Bulletin 13 (1981), 33-38.
  • S. Montgomery, Prime ideals in fixed rings, Comm. in Algebra 9 (1981), 423-449.
  • M. Cohen and S. Montgomery, Trace functions for finite automorphism groups of rings, Archiv der Mathematik 35 (1980), 516-527.
  • S. Montgomery, Automorphism groups of rings with no nilpotent elements, J. of Algebra 60 (1979), 238-248.
  • M. Cohen and S. Montgomery, The normal closure of a semiprime ring, in Ring Theory: Proceedings of the 1978 Antwerp Conference, Marcel Dekker Lecture Notes in Mathematics 51 (1979), 43-59.
  • S. Montgomery, Invariant subgroups of rings with involution, Canadian J. Math. 30 (1978), 350-357.
  • S. Montgomery, Outer automorphisms of semi-prime rings, London Math. Soc. Journal 18 (1978), 209-220. 16
  • J. W. Fisher and S. Montgomery, Semiprime skew group rings, J. of Algebra 52 (1978), 241-247.
  • S. Montgomery and D. S. Passman, Crossed products over prime rings, Israel J. Math. 31 (1978), 224-256.
  • W. S. Martindale, III and S. Montgomery, Fixed elements of Jordon automorphisms of associative rings, Pacific J. Math. 72 (1977), 181-196.
  • S. Montgomery, The Jacobson radical and fixed rings of automorphisms, Comm. in Algebra 4 (1976), 459-465.
  • S. Montgomery, A structure theorem and a positive-definiteness condition in rings with involution, J. of Algebra 43 (1976), 181-192.
  • S. Montgomery and M. K. Smith, Algebras with a separable subalgebra whose centralizer satisfies a polynomial identity, Communications in Algebra 3 (1975), 151 168.
  • S. Montgomery, Centralizers of separable subalgebras, Michigan Math. J. 22 (1975), 15-24.
  • M. Chacron, I. N. Herstein, and S. Montgomery, Structure of a certain class of rings with involution, Canadian J. Math. 27 (1975), 1114-1126.
  • M. Cohen and S. Montgomery, Semi-simple Artinian rings of fixed points, Canadian Math. Bulletin 18 (1975), 189-190.
  • S. Montgomery, Rings with involution in which every trace is nilpotent or regular, Canadian J. Math. 26 (1974), 130-137.
  • S. Montgomery, Rings of quotients for a class of special Jordan rings, J. of Algebra 31 (1974), 154-165.
  • S. Montgomery, Chain conditions on symmetric elements, AMS Proceedings 46 (1974), 325-331.
  • S. Montgomery, Centralizers satisfying polynomial identities, Israel J. Math. 18 (1974), 207-219.
  • I. N. Herstein and S. Montgomery, A generalization of a theorem of Jacobson II, Pacific J. Math. 43 (1973), 233-240.
  • S. Montgomery, Invertible and regular elements in rings with involution, J. of Algebra 25 (1973), 390-400.
  • S. Montgomery, Algebraic algebras with involution, AMS Proceedings 31 (1972), 368- 372.
  • C. Lanski and S. Montgomery, Lie structure of prime rings of characterists 2, Pacific  J. Math. 42 (1972), 117-136.
  • I. N. Herstein and S. Montgomery, A note on division rings with involution, Michigan Math. J. 18 (1971), 75-79.
  • S. Montgomery, Polynomial identity algebras with involution, AMS Proceedings 27 (1971), 53-56.
  • S. Montgomery, A generalization of a theorem of Jacobson, AMS Proceedings 31 (1971), 366-370.
  • T. S. Erickson and S. Montgomery, The prime radical in special Jordan rings, AMS Transactions 156 (1971), 155-164.
  • S. Montgomery, Lie structure of simple rings of characteristic 2, J. of Algebra 15 (1970), 387-407.
  • S. Montgomery, Left and right inverses in group algebras, AMS Bulletin 75 (1969), 539-540.