Results 231 to 240 of about 57,174 (264)

Normalizers of subgroups of division rings

Journal of Group Theory, 2008
Let \(D\) be a division ring with centre \(F\), \(G\) be a subgroup of the multiplicative group \(D^*\) of \(D\). Denote by \(H=N_{D^*}(G)\) the normalizer of \(G\) in \(D^*\) and by \(E=C_D(G)\) the centralizer of \(G\) in \(D\). \textit{M. Shirvani}, [in J. Algebra 294, No. 1, 255-277 (2005; Zbl 1088.16024)], was able to compute \(H\) precisely for \(
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On a Sheaf of Division Rings^*

Canadian Mathematical Bulletin, 1975
R. Arens and I. Kaplansky ([1]) call a ring A biregular if every two sided principal ideal of A is generated by a central idempotent and a ring A strongly regular if for any a in A there exists b in A such that a=a2b. In ([1], Sections 2 and 3), a lot of interesting properties of a biregular ring and a strongly regular ring are given.
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Alternative Division Rings, II

2002
In this chapter we prove Theorem 17.3. Our goal is to show that the Cayley-Dickson algebras defined in (9.8) are the only non-associative alternative division rings. This result was first proved in [17] and [56] by R. Bruck and E. Kleinfeld. See also [3], [74] and [87]. In the proof we give here, the characteristic does not play any role.
Jacques Tits, Richard M. Weiss
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The word problem for division rings

Journal of Symbolic Logic, 1973
In this paper we prove that the word problem for division rings is recursively unsolvable. Our proof relies on the corresponding result for groups [7], [28], and makes essential use of P. M. Cohn's recent work [11], [13], [15], [16] on division rings.The word problem for groups is usually formulated in terms of group presentations or finitely presented
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On the Commutativity of Certain Division Rings

Canadian Journal of Mathematics, 1953
Formerly Hua [1] proved that if A is a division ring with centre Z and if there exists a natural number n such that an ∈ Z for every a ∈ A, then A is commutative; this generalizes Wedderburn's theorem on finite division rings. Another
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Combinatorial Nullstellensatz over division rings

Journal of Algebraic Combinatorics, 2023
Elad Paran
exaly  

On the Lie Ring of a Division Ring

The Annals of Mathematics, 1954
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A Note on Division Rings

American Journal of Mathematics, 1947
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Division Rings of Fractions for Group Rings

Communications on Pure and Applied Mathematics, 1970
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Multiplicative Subgroups in Weakly Locally Finite Division Rings

Acta Mathematica Vietnamica, 2021
Bui Xuan Hai, Huynh Viet Khanh
exaly