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The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let $K$ be a unital commutative ring, not necessarily a field. Given a unital $K$ -algebra $S$ , where $K$ is contained in the center of $S$ , $n \in ℕ$ , the goal of this paper is to study the question: when can a homomorphism $φ : M_{n} (K) \to M_{n} (S)$ be extended to an inner automorphism of $M_{n} (S)$ ? As an application of main results presented in the paper, it is proved that if $S$ is a semilocal...

A note on the simplicity of skew polynomial rings of derivation type

Michael Gr. Voskoglou (2004)

Acta Mathematica Universitatis Ostraviensis

À propos des théories de Galois finies et infinies

R. Moors (1974)

Colloquium Mathematicae

A question on the discriminants of involutions of central division algebras.

R. Sridharan, R. Parimala, V. Suresh (1993)

Mathematische Annalen

A Reduction Theorem for the Primitivity of Tensor Products.

Richard Resco (1980)

Mathematische Zeitschrift

A remark on power series rings.

Paul M. Cohn (1992)

Publicacions Matemàtiques

A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.

A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.

Bernhard Keller (1988)

Mathematische Zeitschrift

A Remark on tilting theory and DG algebras.

Bernhard Keller (1993)

Manuscripta mathematica

A result on vanishing derivations for commutators on right ideals.

De Filippis, Vincenzo (2005)

Mathematica Pannonica

A structure sheaf on the projective spectrum of a graded fully bounded Noetherian ring.

Samir Mahmoud, S. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

A theoreme on derivations in semiprime rings.

Qing Deng (1995)

Collectanea Mathematica

A unified approach to the Armendariz property of polynomial rings and power series rings

Tsiu-Kwen Lee, Yiqiang Zhou (2008)

Colloquium Mathematicae

A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever $(\sum_{i \geq 0} a_{i} x^{i}) (\sum_{j \geq 0} b_{j} x^{j}) = 0$ in R[x] (resp., in R[[x]]), then $a_{i} b_{j} = 0$ for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism σ of a ring...

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A note on perfect modules over crossed products

A Note on Posner s Theorem with Generalized Derivations on Lie Ideals

A note on p.q.-Baer modules.

A note on semiprime rings with derivation.

A Note on Skew Polynomial Rings

A note on Skolem-Noether algebras