Results 221 to 230 of about 57,174 (264)
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A Survey on Free Objects in Division Rings and in Division Rings with an Involution
Communications in Algebra, 2012Let D be a division ring with center k, and let D † be its multiplicative group. We investigate the existence of free groups in D †, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D †.
M Shirvani
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Canadian Journal of Mathematics, 1969
The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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On Conjugates in Division Rings
Canadian Journal of Mathematics, 1958Let D be a non-commutative division ring with centre C, and let Δ be a proper division subring not contained in C. In (4) Cartan raised the question: is it ever possible for each inner automorphism of D to induce an automorphism of Δ? As is well-known, Cartan (4, Théorème 4) with the aid of his Galois Theory answered this negatively in case D is a ...
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Canadian Journal of Mathematics, 1951
The object of this note is to prove the following theorem. THEOREM. Let A be a division ring with centre Z, and suppose that for every x in A, some power (depending on x) is in . Then A is commutative.
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The object of this note is to prove the following theorem. THEOREM. Let A be a division ring with centre Z, and suppose that for every x in A, some power (depending on x) is in . Then A is commutative.
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Equations in Division Rings--A Survey
The American Mathematical Monthly, 1989(1989). Equations in Division Rings—A Survey. The American Mathematical Monthly: Vol. 96, No. 3, pp. 220-232.
J. Lawrence, G. E. Simons
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Subnormal Subgroups of Division Rings
Canadian Journal of Mathematics, 1963Let K be a division ring. A subgroup H of the multiplicative group K′ of K is subnormal if there is a finite sequence (H = A0, A1, . . . , An = K′) of subgroups of K′ such that each Ai is a normal subgroup of Ai+1. It is known (2, 3) that if H is a subdivision ring of K such that H′ is subnormal in K′, then either H = K or H is in the centre Z(K) of K.
Herstein, I. N., Scott, W. R.
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Thoracoscopic division of vascular rings
Journal of Pediatric Surgery, 2017Vascular rings are traditionally treated via an open thoracotomy. In recent years the use of thoracoscopy has increased. Herein we report our experience with thoracoscopic division of vascular rings in pediatric patients.We reviewed all patients who underwent thoracoscopic or open division of a vascular ring at our institution between 2007 and 2015. We
Kevin M, Riggle +2 more
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Proceedings of the American Mathematical Society, 1987
A V-ring is a ring for which every simple right module is injective. If D is a division algebra over a field k, then an \(n\times n\) matrix A over D is called totally transcendental over k if f(A) is invertible for every non-zero polynomial f over k.
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A V-ring is a ring for which every simple right module is injective. If D is a division algebra over a field k, then an \(n\times n\) matrix A over D is called totally transcendental over k if f(A) is invertible for every non-zero polynomial f over k.
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Group Rings and Division Rings
1984Continuing the work in [ll],[l2] we study division algebras D = k(G) over a field k which are generated by some polycyclic-by-finite subgroup G of the multiplicative group D* of D. We discuss a specific class of examples of such division algebras that can be thought of as multiplicative analogs of the Weyl field.
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