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On centralizers of semiprime rings

Borut Zalar (1991)

Commentationes Mathematicae Universitatis Carolinae

Let 𝒦 be a semiprime ring and T : 𝒦 → 𝒦 an additive mapping such that T ( x 2 ) = T ( x ) x holds for all x ∈ 𝒦 . Then T is a left centralizer of 𝒦 . It is also proved that Jordan centralizers and centralizers of 𝒦 coincide.

On computation of minimal free resolutions over solvable polynomial algebras

Huishi Li (2015)

Commentationes Mathematicae Universitatis Carolinae

Let A = K [ a 1 , ... , a n ] be a (noncommutative) solvable polynomial algebra over a field K in the sense of A. Kandri-Rody and V. Weispfenning [Non-commutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), 1–26]. This paper presents a comprehensive study on the computation of minimal free resolutions of modules over A in the following two cases: (1) A = ⨁ p ∈ ℕ A p is an ℕ -graded algebra with the degree-0 homogeneous part A 0 = K ; (2) A is an ℕ -filtered algebra with the filtration { F p A } p ∈ ℕ determined by a positive-degree...

On G -disconnected injective models

Marek Golasiński (2003)

Annales de l’institut Fourier

Let G be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the G -connected case is incorrect because of an error concerning algebraic properties. In the G -disconnected case the orbit category 𝒪 ( G ) was originally replaced by the category 𝒪 ( G , X ) with one object for each component of each fixed point simplicial subsets X H of a G -simplicial set X , for all subgroups H ⊆ G . We redefine the equivariant minimality and redevelop some results on the rational homotopy...

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