Journal article
On Nilpotency of the Separating Ideal of a Derivation
Proceedings of the American Mathematical Society, v 117(1), pp 167-174
01 Jan 1993
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Abstract
We prove that the separating ideal S(D) of any derivation D on a commutative unital algebra B is nilpotent if and only if$S(D) \cap (\bigcap R^n)$is a nil ideal, where R is the Jacobson radical of B. Also we show that any derivation D on a commutative unital semiprime Banach algebra B is continuous if and only if$\bigcap(S(D))^n = \{0\}$. Further we show that the set of all nilpotent elements of S(D) is equal to$\bigcap(S(D) \cap P)$, where the intersection runs over all nonclosed prime ideals of B not containing S(D). As a consequence, we show that if a commutative unital Banach algebra has only countably many nonclosed prime ideals then the separating ideal of a derivation is nilpotent.
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Details
- Title
- On Nilpotency of the Separating Ideal of a Derivation
- Creators
- Ramesh V. Garimella
- Publication Details
- Proceedings of the American Mathematical Society, v 117(1), pp 167-174
- Publisher
- American Mathematical Society
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1993KG71100024
- Scopus ID
- 2-s2.0-84966213166
- Other Identifier
- 991021861619504721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied