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On a subset with nilpotent values in a prime ring with derivation

Vincenzo De Filippis (2002)

Bollettino dell'Unione Matematica Italiana

Let R be a prime ring, with no non-zero nil right ideal, d a non-zero drivation of R , I a non-zero two-sided ideal of R . If, for any x , y I , there exists n = n x , y 1 such that d x , y - x , y n = 0 , then R is commutative. As a consequence we extend the result to Lie ideals.

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

We study McCoy’s theorem to the skew Hurwitz series ring ( HR , ω ) for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring R satisfies McCoy’s theorem of skew Hurwitz series.

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 clean ideals.

Chen, Huanyin, Chen, Miaosen (2003)

International Journal of Mathematics and Mathematical Sciences

On commutative twisted group rings

Todor Zh. Mollov, Nako A. Nachev (2005)

Czechoslovak Mathematical Journal

Let G be an abelian group, R a commutative ring of prime characteristic p with identity and R t G a commutative twisted group ring of G over R . Suppose p is a fixed prime, G p and S ( R t G ) are the p -components of G and of the unit group U ( R t G ) of R t G , respectively. Let R * be the multiplicative group of R and let f α ( S ) be the α -th Ulm-Kaplansky invariant of S ( R t G ) where α is any ordinal. In the paper the invariants f n ( S ) , n { 0 } , are calculated, provided G p = 1 . Further, a commutative ring R with identity of prime characteristic p is said...

On E k -rings

Alessandra Cherubini, Ada Varisco (1988)

Czechoslovak Mathematical Journal

On feebly nil-clean rings

Marjan Sheibani Abdolyousefi, Neda Pouyan (2024)

Czechoslovak Mathematical Journal

A ring R is feebly nil-clean if for any a R there exist two orthogonal idempotents e , f R and a nilpotent w R such that a = e - f + w . Let R be a 2-primal feebly nil-clean ring. We prove that every matrix ring over R is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.

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