Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

Varieties of solvable Lie rings of finite width

1998 ◽  
Vol 63 (5) ◽  
pp. 569-574
Author(s):  
D. S. Ananichev ◽  
M. V. Volkov
Keyword(s):  
Finite Width ◽  
Lie Rings

scholarly journals Color Lie rings and PBW deformations of skew group algebras

2019 ◽  
Vol 518 ◽  
pp. 211-236
Author(s):  
S. Fryer ◽  
T. Kanstrup ◽  
E. Kirkman ◽  
A.V. Shepler ◽  
S. Witherspoon
Keyword(s):  
Group Algebras ◽  
Lie Rings ◽  
Skew Group Algebras

On New Analogs of Some Classical Group Theoretical Results in Lie Rings

2017 ◽  
pp. 197-213
Author(s):  
L. A. Kurdachenko ◽  
A. A. Pypka ◽  
I. Ya. Subbotin
Keyword(s):  
Classical Group ◽  
Lie Rings ◽  
Theoretical Results

scholarly journals Paul Moritz Cohn. 8 January 1924 — 20 April 2006

2014 ◽  
Vol 60 ◽  
pp. 127-150 ◽  
Author(s):  
George Bergman ◽  
Trevor Stuart
Keyword(s):  
Group Theory ◽  
Trinity College ◽  
London Mathematical Society ◽  
Ring Theory ◽  
Concentration Camps ◽  
Entrance Examination ◽  
English School ◽  
Lie Rings ◽  
Chicken Farm ◽  
Work First

Paul Cohn was born in Hamburg, where he lived until he was 15 years of age. However, in 1939, after the rise of the Nazis and the growing persecution of the Jews, his parents, James and Julia Cohn, sent him to England by Kindertransport. They remained behind and Paul never saw them again; they perished in concentration camps. In England, being only 15 years old, he was directed to work first on a chicken farm but later as a fitter in a London factory. His academic talents became clear and he was encouraged by the refugee committee in Dorking and by others to continue his education by studying for the English School Certificate Examinations to sit the Cambridge Entrance Examination. He was awarded an Exhibition to study mathematics at Trinity College. After receiving his PhD in 1951, Paul Cohn went from strength to strength in algebra and not only became a world leader in non-commutative ring theory but also made important contributions to group theory, Lie rings and semigroups. He was much admired, and he travelled widely to collaborate with other algebraists. Moreover, he was a great supporter of the London Mathematical Society, serving as its President from 1982 to 1984.

Isoclinism of pairs of Lie rings

2019 ◽  
Vol 19 (02) ◽  
pp. 2050031 ◽  
Author(s):  
Mahin Heidari ◽  
Mohammad Reza Rismanchian
Keyword(s):  
Lie Algebras ◽  
Lie Rings

The concept of isoclinism on the class of groups was introduced by Philip Hall in 1940. Then, in 1993, Moneyhun used this concept on Lie algebras. In this paper, we study the notion of isoclinism on pairs of Lie rings, and some results are obtained when two isoclinic pairs of Lie rings are given. In particular, we prove that every isoclinism class of pairs of Lie rings contains at least one stem pair.

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