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Displaying similar documents to “On groups of similitudes in associative rings”

Centralizers on semiprime rings

Joso Vukman (2001)

Commentationes Mathematicae Universitatis Carolinae

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The main result: Let R be a 2 -torsion free semiprime ring and let T : R R be an additive mapping. Suppose that T ( x y x ) = x T ( y ) x holds for all x , y R . In this case T is a centralizer.

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set S ( X ) such that its complement S ( X ) is σ -porous and such that for each A and each x ˜ D , the set of solutions of the best approximation problem x ˜ - z min , z A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a p -extension of k, k n the nth layer of k / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k / k be a p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k / k . Then there exist integers λ = λ ( k / k ) 0 , μ = μ ( k / k ) 0 , ν = ν ( k / k ) , and n₀ ≥ 0...