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Volume 83 - Issue 2 - October 2007

Contents

Research Article

  • Recognizing powers in nilpotent groups and nilpotent images of free groups
  • Part of:
  • Gilbert Baumslag
  • Published online by Cambridge University Press: 09 April 2009, pp. 149-156
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    An element in a free group is a proper power if and only if it is a proper power in every nilpotent factor group. Moreover there is an algorithm to decide if an element in a finitely generated torsion-free nilpotent group is a proper power.

  • Transcendental meromorphic solutions of some algebraic differential equations
  • Part of:
  • Katsuya Ishizaki, Nobushige Toda
  • Published online by Cambridge University Press: 09 April 2009, pp. 157-180
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    In this paper we treat transcendental meromorphic solutions of some algebraic differential equations. We consider the number of distinct transcendental meromorphic solutions. Algebraic relations between meromorphic solutions and comparisons of the growth of transcendental meromorphic solutions are also discussed.

  • The block structure of complete lattice ordered effect algebras
  • Part of:
  • Gejza Jenča
  • Published online by Cambridge University Press: 09 April 2009, pp. 181-216
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    We prove that every for every complete lattice-ordered effect algebra E there exists an orthomodular lattice O(E) and a surjective full morphism øE: O(E) → E which preserves blocks in both directions: the (pre)imageofa block is always a block. Moreover, there is a 0, 1-lattice embedding : E → O(E).

  • On the asymptotic behaviour of associated primes of generalized local cohomology modules
  • Part of:
  • Kazem Khashyarmaneshs, Ahmad Abbasi
  • Published online by Cambridge University Press: 09 April 2009, pp. 217-226
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    Let M and N be finitely generated and graded modules over a standard positive graded commutative Noetherian ring R, with irrelevant ideal R+. Let be the nth component of the graded generalized local cohomology module . In this paper we study the asymptotic behavior of Assf R+ () as n → –∞ whenever k is the least integer j for which the ordinary local cohomology module is not finitely generated.

  • Large doubly transitive orbits on a line
  • Part of:
  • Alessandro Montinaro
  • Published online by Cambridge University Press: 09 April 2009, pp. 227-270
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    Projective planes of order n with a coUineation group admitting a 2-transitive orbit on a line of length at least n/2 are investigated and new examples are provided.

  • Stable perturbation in Banach algebras
  • Part of:
  • Yifeng Xue
  • Published online by Cambridge University Press: 09 April 2009, pp. 271-284
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    Let be a unital Banach algebra. Assume that a has a generalized inverse a+. Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.

  • Baer and quasi-Baer properties of group rings
  • Part of:
  • Zhong Yi, Yiqiang Zhou
  • Published online by Cambridge University Press: 09 April 2009, pp. 285-296
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    A ring R is said to be a Baer (respectively, quasi-Baer) ring if the left annihilator of any nonempty subset (respectively, any ideal) of R is generated by an idempotent. It is first proved that for a ring R and a group G, if a group ring RG is (quasi-) Baer then so is R; if in addition G is finite then |G|–1 € R. Counter examples are then given to answer Hirano's question which asks whether the group ring RG is (quasi-) Baer if R is (quasi-) Baer and G is a finite group with |G|–1 € R. Further, efforts have been made towards answering the question of when the group ring RG of a finite group G is (quasi-) Baer, and various (quasi-) Baer group rings are identified. For the case where G is a group acting on R as automorphisms, some sufficient conditions are given for the fixed ring RG to be Baer.

Front matter

  • JAZ volume 83 issue 2 Cover and Front matter
  • Published online by Cambridge University Press: 09 April 2009, pp. f1-f2
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Back matter

  • JAZ volume 83 issue 2 Cover and Back matter
  • Published online by Cambridge University Press: 09 April 2009, pp. b1-b2
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