Access the full text.
Sign up today, get DeepDyve free for 14 days.
HE Bell, MN Daif (1995)
On derivations and commutativity in prime ringsActa Math. Hungar., 66
M Henriksen, FA Smith (1982)
Some properties of positive derivations on f-ringsContemp. Math., 8
P. Colville, G. Davis, K. Keimel (1977)
Positive derivations on f-ringsJournal of the Australian Mathematical Society, 23
EC Posner (1957)
Derivations in prime ringsProc. Am. Math. Soc., 8
V. Filippis (2004)
On derivations and commutativity in prime ringsInt. J. Math. Math. Sci., 2004
R DeMarr (1967)
On partially ordering operator algebrasCanad. J. Math., 19
M Ebrahimi, H Pajoohesh (2004)
Composition of derivations on (semi)prime $$\ell $$ ℓ -ringsH. Kyungpook Math. J., 44
P Colville, G Davis, K Keimel (1977)
Positive derivations on $$f$$ f -ringsJ Aust. Math. Soc. Ser. A, 23
M. Darnel (1994)
Theory of Lattice-Ordered Groups
S Andima, H Pajoohesh (2010)
Commutativity of rings with derivationsActa Math. Hungar., 128
T. Lam (2002)
A first course in noncommutative rings
N. Jacobson (1945)
Structure theory for algebraic algebras of bounded degreeAnn. Math. (2), 46
S Steinberg (2010)
Lattice-Ordered Rings and Modules
Cheng-Jun Hou, Wenmin Zhang, Qing Meng (2010)
A note on (a,)(a,)-derivations?Linear Algebra and its Applications
IN Herstein (1978)
A note on derivationsCanad. Math. Bull., 21
(1974)
Algebra
LO Chung, J Luh (1984)
Nilpotency of derivations on an idealProc. Am. Math. Soc., 90
(1967)
Lattice Theory, 3rd edn
JH Mayne (1982)
Ideals and centralizing mappings in prime ringsProc. Am. Math. Soc., 86
A. Bigard, Klaus Keimel, S. Wolfenstein (1977)
Groupes et anneaux réticulés
In 1978 I. N. Herstein proved that a prime ring $$R$$ R of characteristic not two with nonzero derivation $$d$$ d satisfying $$d(x)d(y)=d(y)d(x)$$ d ( x ) d ( y ) = d ( y ) d ( x ) for all $$x,y\in R$$ x , y ∈ R is commutative, and in 1995 Bell and Daif showed that $$d(xy)=d(yx)$$ d ( x y ) = d ( y x ) implies commutativity. We extend the Bell–Daif theorem to lattice-ordered prime rings with a positive derivation satisfying the property on a one-sided $$L$$ L -ideal and interpret these conditions for higher derivations in prime $$d$$ d -rings and in semiprime $$f$$ f -rings. Our key tool is that every positive derivation nilpotent on a one-sided $$L$$ L -ideal of a semiprime $$\ell $$ ℓ -ring is zero on that ideal.
Positivity – Springer Journals
Published: Dec 11, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.