Results 51 to 60 of about 507 (91)
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 263-266, 1997., 1995 Let R be a ring A bi‐additive symmetric mapping d : R × R → R is called a symmetric bi‐derivation if, for any fixed y ∈ R, the mapping x → D(x, y) is a derivation. The purpose of this paper is to prove the following conjecture of Vukman. Let R be a noncommutative prime ring with suitable characteristic restrictions, and let D : R × R → R and f : x → D ...
Qing Deng
wiley +1 more source
Open Mathematics, 2017 In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring.
Banič Iztok
doaj +1 more source
A note on semiprime rings with derivation
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 413-415, 1997., 1996 Let R be a 2‐torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D : R → R a derivation. If d[x, y] + [x, y] ∈ Z or d[x, y] − [x, y] ∈ Z for all x, y ∈ I, then R is commutative.
Motoshi Hongan
wiley +1 more source
Multiplicative generalized derivations on Lie ideals in semiprime rings II
, 2017 Let R be a semiprime ring and L is a Lie ideal of R such that L 6 Z.R/. A map F WR!R is called a multiplicative generalized derivation if there exists a map d WR!R such that F.xy/D F.x/yCxd.y/; for all x;y 2 R: In the present paper, we shall prove that d
E. Koç, Ö. Gölbasi
semanticscholar +1 more source
A Generalized Higher Reverse Left (respectively Right) Centralizer on Prime Gamma-Rings
Mathematical theory and modelling, 2019 This study introduces the concepts of generalized higher reverse left (respectively right) centralizer , Jordan generalized higher reverse left (respectively right) centralizer and Jordan triple generalized higher reverse left (respectively right ...
Fawaz Ra'ad Jarullah, S. M. Salih
semanticscholar +1 more source
Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a ...
Kholood Alnefaie, Pramita Mishra
wiley +1 more source
A Note About the Nowicki Conjecture on Weitzenböck Derivations [PDF]
, 2009 2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant ...
Bedratyuk, Leonid
core
Divergences on projective modules and non-commutative integrals
, 2010 A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented.
Bernshtein I. N. +3 more
core +1 more source
A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi +4 more
wiley +1 more source
Weitzenböck Derivations and Classical Invariant Theory: I. Poincaré Series [PDF]
, 2010 2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.By using classical invariant theory approach, formulas for computation of the Poincaré series of the kernel of linear locally nilpotent derivations are ...
Bedratyuk, Leonid
core