Displaying similar documents to “Maximal Orders in an Azumaya Algebra over a Von Neumann Regular Ring”

Solutions of minus partial ordering equations over von Neumann regular rings

Yu Guan, Zhaojia Tong (2015)

Open Mathematics

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In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

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A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vaš (2007)

Mathematica Bohemica

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We prove that a finite von Neumann algebra 𝒜 is semisimple if the algebra of affiliated operators 𝒰 of 𝒜 is semisimple. When 𝒜 is not semisimple, we give the upper and lower bounds for the global dimensions of 𝒜 and 𝒰 . This last result requires the use of the Continuum Hypothesis.

Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher

Michael Skeide (2006)

Banach Center Publications

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The category of von Neumann correspondences from 𝓑 to 𝓒 (or von Neumann 𝓑-𝓒-modules) is dual to the category of von Neumann correspondences from 𝓒' to 𝓑' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem...

On the Neumann problem with L¹ data

J. Chabrowski (2007)

Colloquium Mathematicae

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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.

On the Neumann problem with combined nonlinearities

Jan Chabrowski, Jianfu Yang (2005)

Annales Polonici Mathematici

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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.