Ashraf, Mohammad, Ali, Asma, and Ali, Shakir. "$(\sigma ,\tau )$-derivations on prime near rings." Archivum Mathematicum 040.3 (2004): 281-286. <http://eudml.org/doc/249295>.
@article{Ashraf2004,
abstract = {There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation namely $(\sigma ,\tau )$- derivation where $\sigma ,\tau $ are automorphisms of the near-ring. Finally, it is shown that under appropriate additional hypothesis a near-ring must be a commutative ring.},
author = {Ashraf, Mohammad, Ali, Asma, Ali, Shakir},
journal = {Archivum Mathematicum},
keywords = {prime near-ring; derivation; $\sigma $-derivation; $(\sigma , \tau )$-derivation; $(\sigma , \tau )$-commuting derivation; prime near-rings; commuting derivations; commutativity theorems},
language = {eng},
number = {3},
pages = {281-286},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$(\sigma ,\tau )$-derivations on prime near rings},
url = {http://eudml.org/doc/249295},
volume = {040},
year = {2004},
}
TY - JOUR
AU - Ashraf, Mohammad
AU - Ali, Asma
AU - Ali, Shakir
TI - $(\sigma ,\tau )$-derivations on prime near rings
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 3
SP - 281
EP - 286
AB - There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation namely $(\sigma ,\tau )$- derivation where $\sigma ,\tau $ are automorphisms of the near-ring. Finally, it is shown that under appropriate additional hypothesis a near-ring must be a commutative ring.
LA - eng
KW - prime near-ring; derivation; $\sigma $-derivation; $(\sigma , \tau )$-derivation; $(\sigma , \tau )$-commuting derivation; prime near-rings; commuting derivations; commutativity theorems
UR - http://eudml.org/doc/249295
ER -
