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Derivations and Leibniz differences on rings: II.
- Source :
-
Aequationes Mathematicae . Dec2019, Vol. 93 Issue 6, p1127-1138. 12p. - Publication Year :
- 2019
-
Abstract
- In an earlier paper we discussed the composition of derivations of order 1 on a commutative ring R, showing that (i) the composition of n derivations of order 1 yields a derivation of order at most n, and (ii) under additional conditions on R the composition of n derivations of order exactly 1 forms a derivation of order exactly n. In the present paper we consider the composition of derivations of any orders on rings. We show that on any commutative ring R the composition of a derivation of order at most n with a derivation of order at most m results in a derivation of order at most n + m . If R is an integral domain of sufficiently large characteristic, then the composition of a derivation of order exactly n with a derivation of order exactly m results in a derivation of order exactly n + m . As in the previous paper, the results are proved using Leibniz difference operators. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIFFERENCE operators
*INTEGRAL domains
*COMMUTATIVE rings
*COMMUTATIVE algebra
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 93
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 139694007
- Full Text :
- https://doi.org/10.1007/s00010-018-0630-z