Results 61 to 70 of about 1,309,327 (169)

DERIVATIONS OF PRIME AND SEMIPRIME RINGS [PDF]

Journal of the Korean Mathematical Society, 2009
Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x)) n = xy + yx for all x,y 2 I, then R is commutative. (ii) If charR 6 2 and (d(x)y + xd(y) + d(y)x + yd(x)) n i (xy + yx) is central for all x,y 2 I, then R is commutative.
Argac, Nurcan, Inceboz, Hulya G.
openaire   +2 more sources

Coweakly Uniserial Modules and Rings Whose (2‐Generated) Modules Are Coweakly Uniserial

Journal of Mathematics, Volume 2025, Issue 1, 2025.
A module is called weakly uniserial if for any two its submodules at least one of them is embedded in the other. This is a nontrivial generalization of uniserial modules and rings. Here, we introduce and study the dual of this concept. In fact, an R‐module M is called coweakly uniserial if for any submodules N, K of M, HomR(M/N, M/K) or HomR(M/K, M/N ...
M. M. Oladghobad, R. Beyranvand, Faranak Farshadifar   +2 more
wiley   +1 more source

A note on derivations in semiprime rings

International Journal of Mathematics and Mathematical Sciences, 2005
We prove in this note the following result. Let n>1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D:R→R such that D(xn)=∑j=1nxn−jD(x)xj−1 is fulfilled for all x∈R.
Joso Vukman, Irena Kosi-Ulbl
doaj   +1 more source

Jordan derivations on semiprime rings [PDF]

Proceedings of the American Mathematical Society, 1988
I. N. Herstein has proved that any Jordan derivation on a 2 2 -torsion free prime ring is a derivation. In this paper we prove that Herstein’s result is true in 2 2 -torsion free semiprime rings. This result makes it possible for us to prove that any linear Jordan derivation on a semisimple Banach algebra is continuous,
openaire   +1 more source

A Unified Approach to Generalizing π‐Extending and π‐Baer Rings

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper introduces and examines the right essentially π‐Baer ring property, which serves as a new extension of the π‐extending and π‐Baer ring conditions. The initial phase of the study involves the development of several foundational results. The subsequent phase of the study involves the exploration of the transfer of the right essentially π‐Baer ...
Yeliz Kara, Ali Jaballah
wiley   +1 more source

On Maps of Period 2 on Prime and Semiprime Rings

International Journal of Mathematics and Mathematical Sciences, 2014
A map f of the ring R into itself is of period 2 if f2x=x for all x∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized ...
H. E. Bell, M. N. Daif
doaj   +1 more source

On a theorem of McCoy [PDF]

Mathematica Bohemica
We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
doaj   +1 more source

On Rings Whose Simple Singular R-Modules Are Flat, I [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2010
In this paper we investigate von Neumann regularity of rings whose simple singular right R-modules are flat. It is proved that a ring R is strongly regular if and only if R is a semiprime right quasi-duo ring whose simple singular right R-modules are ...
Raida Mahmood, Abdullah Abdul-Jabbar
doaj   +1 more source

A Note on Skew Derivations and Antiautomorphisms of Prime Rings

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this article, we investigate the behavior of a prime ring which admits a skew derivation satisfying certain functional identities involving an antiautomorphism. We employ tools such as generalized identities and commutativity‐preserving maps to analyze these rings.
Faez A. Alqarni, Nadeem U. R. Rehman, Hafedh Alnoghashi, Junaid Nisar, Omar Al-Mallah, Ali Jaballah   +5 more
wiley   +1 more source

On rings of quotients of semiprime $\Gamma$-rings [PDF]

Miskolc Mathematical Notes, 2012
WOS ...
Koc, Emine, Golbasi, Oznur
openaire   +3 more sources