# DERIVATIONS ON SUBRINGS OF MATRIX RINGS

• Chun, Jang-Ho (Department of Mathematics, Yeungnam University) ;
• Park, June-Won (Department of Mathematics, Kyungil University)
• Published : 2006.08.01
• 72 18

#### Abstract

For a lower niltriangular matrix ring $A=NT_n(K)(n{\geq}3)$, we show that every derivation of A is a sum of certain diagonal, trivial extension and strongly nilpotent derivation. Moreover, a strongly nilpotent derivation is a sum of an inner derivation and an uaz-derivation.

#### Keywords

derivations;diagonal derivations;strongly nilpotent derivations;inner derivations

#### References

1. S. A. Amitsur, Extension of derivations to central simple algebras, Comm. Algebra 10 (1982), no. 8, 797-803 https://doi.org/10.1080/00927878208822750
2. J. H. Chun and J. W. Park, Prime ideals of subrings of matrix rings, Commun. Korean Math. Soc. 19 (2004), no. 2, 211-217 https://doi.org/10.4134/CKMS.2004.19.2.211
3. R. Dubisch and S. Perlis, On total nilpotent algebra, Amer. J. Math. 73 (1951), 439-452 https://doi.org/10.2307/2372186
4. I. N. Herstein, Noncommutative rings, The Mathematical Association of America, 1968
5. V. M. Levchuk, Automorphisms of certain nilpotent matrix groups and rings, Dokl. Akad. Nauk SSSR 222 (1975), no. 6, 1279-1282
6. V. M. Levchuk, Connections between the unitriangular group and certain rings. II. Groups of automorphisms, Sibirsk. Mat. Zh. 24 (1983), no. 4, 64-80
7. A. Nowicki, Derivations of special subrings of matrix rings and regular graph, Tsukuba J. Math. 7 (1983), no. 2, 281-297 https://doi.org/10.21099/tkbjm/1496159826
8. F. Kuzucuoglu and V. M. Levchuk, The automorphism group of certain radical matrix rings, J. Algebra 243 (2001), no. 2, 473-485 https://doi.org/10.1006/jabr.2001.8864

#### Cited by

1. DERIVATIONS OF THE LOCALLY NILPOTENT MATRIX RINGS vol.09, pp.05, 2010, https://doi.org/10.1142/S0219498810004154
2. Derivations of a matrix ring containing a subring of triangular matrices vol.55, pp.11, 2011, https://doi.org/10.3103/S1066369X1111003X
3. Derivations of some classes of matrix rings vol.16, pp.02, 2017, https://doi.org/10.1142/S021949881750027X
4. Elementary equivalence and isomorphisms of locally nilpotent matrix groups and rings vol.79, pp.2, 2009, https://doi.org/10.1134/S1064562409020100
5. JORDAN ISOMORPHISMS OF RADICAL FINITARY MATRIX RINGS vol.09, pp.04, 2010, https://doi.org/10.1142/S0219498810004282
6. Jordan Derivations on Strictly Triangular Matrix Rings vol.18, pp.03, 2011, https://doi.org/10.1142/S1005386711000393