Applying the density theorem for derivations to range inclusion problems

• Autorzy: K. I. Beidar , Matej Brešar
• Języki publikacji: EN

Abstrakty

EN

The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.

Kategorie tematyczne

• 46H99: None of the above, but in this section
• 16N20: Jacobson radical, quasimultiplication
• 16W25: Derivations, actions of Lie algebras
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 138
• Numer: 1
• Strony: 93-100

Daty

wydano

2000

otrzymano

1999-05-18

Twórcy

autor

K. I. Beidar

• Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan.

autor

Matej Brešar

• Department of Mathematics, University of Maribor, Maribor, Slovenia

Bibliografia

• [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
• [2] K. I. Beidar and M. Brešar, Extended Jacobson density theorem for rings with derivations and automorphisms, submitted.
• [3] K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with Generalized Identities, Marcel Dekker, 1996.
• [4] M. Brešar, Derivations on noncommutative Banach algebras II, Arch. Math. (Basel) 61 (1994), 56-59.
• [5] M. Brešar, Derivations mapping into the socle, II, Proc. Amer. Math. Soc. 126 (1998), 181-188.
• [6] M. Brešar and P. Šemrl, On locally linearly dependent operators and derivations, Trans. Amer. Math. Soc. 351 (1999), 1257-1275.
• [7] L. O. Chung and J. Luh, Nilpotency of derivations, Canad. Math. Bull. 26 (1983), 341-346.
• [8] B. Felzenszwalb and C. Lanski, On the centralizers of ideals and nil derivations, J. Algebra 83 (1983), 520-530.
• [9] I. N. Herstein, A note on derivations, Canad. Math. Bull. 21 (1978), 369-370.
• [10] I. N. Herstein, Sui commutatori degli anelli semplici, Rend. Sem. Mat. Fis. Milano 33 (1963), 80-86.
• [11] V. K. Kharchenko, Differential identities of prime rings, Algebra and Logic 17 (1978), 155-168.
• [12] C. Lanski, Derivations nilpotent on subsets of prime rings, Comm. Algebra 20 (1992), 1427-1446.
• [13] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993), 731-734.
• [14] C. Le Page, Sur quelques conditions entraȋnant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 265 (1967), 235-237.
• [15] W. S. Martindale III and C. R. Miers, On the iterates of derivations of prime rings, Pacific J. Math. 104 (1983), 179-190.
• [16] M. Mathieu, Where to find the image of a derivation, in: Banach Center Publ. 30, Inst. Math. Polish Acad. Sci., Warszawa, 1994, 237-249.
• [17] M. Mathieu and G. J. Murphy, Derivations mapping into the radical, Arch. Math. (Basel) 57 (1991), 469-474.
• [18] M. Mathieu and V. Runde, Derivations mapping into the radical, II, Bull. London Math. Soc. 24 (1992), 485-487.
• [19] G. J. Murphy, Aspects of the theory of derivations, in: Banach Center Publ. 30 1994, 267-275.
• [20] V. Pták, Commutators in Banach algebras, Proc. Edinburgh Math. Soc. 22 (1979), 207-211.
• [21] V. Runde, Range inclusion results for derivations on noncommutative Banach algebras, Studia Math. 105 (1993), 159-172.
• [22] A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166-170.
• [23] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264.
• [24] M. P. Thomas, The image of a derivation is contained in the radical, Ann. of Math. 128 (1988), 435-460.
• [25] Yu. V. Turovskiĭ and V. S. Shul'man, Conditions for the massiveness of the range of a derivation of a Banach algebra and of associated differential operators, Mat. Zametki 42 (1987), 305-314 (in Russian).